6x-7=3x^2-9x-7

Solution for 6x-7=3x^2-9x-7 equation:

6x-7=3x^2-9x-7

We move all terms to the left:

6x-7-(3x^2-9x-7)=0

We get rid of parentheses

-3x^2+6x+9x+7-7=0

We add all the numbers together, and all the variables

-3x^2+15x=0

a = -3; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-3)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-3}=\frac{0}{-6}
=0
$