Answer:
The solution to the quadratic equation be:
[tex]x=\frac{5}{3},\:x=-1[/tex]
Step-by-step explanation:
Given the expression
3x² – 2x = 5
Solving with the quadratic formula
[tex]3x^2-2x=5[/tex]
subtract 5 from both sides
[tex]3x^2-2x-5=5-5[/tex]
Simplify
[tex]3x^2-2x-5=0[/tex]
For a quadratic equation of the form ax²+bx+c=0
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
For a = 3, b = -2, c = -5
[tex]x_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-5\right)}}{2\cdot \:3}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-2\right)\pm \:8}{2\cdot \:3}[/tex]
Separate the solutions
[tex]x_1=\frac{-\left(-2\right)+8}{2\cdot \:3},\:x_2=\frac{-\left(-2\right)-8}{2\cdot \:3}[/tex]
solving
[tex]x_1=\frac{-\left(-2\right)+8}{2\cdot \:3}[/tex]
[tex]=\frac{2+8}{2\cdot \:3}[/tex]
[tex]=\frac{10}{6}[/tex]
[tex]=\frac{5}{3}[/tex]
also solving
[tex]x_2=\frac{-\left(-2\right)-8}{2\cdot \:3}[/tex]
[tex]=\frac{2-8}{2\cdot \:3}[/tex]
[tex]=\frac{-6}{2\cdot \:3}[/tex]
[tex]=\frac{-6}{6}[/tex]
[tex]=-\frac{6}{6}[/tex]
[tex]=-1[/tex]
Therefore, the solution to the quadratic equation be:
[tex]x=\frac{5}{3},\:x=-1[/tex]
