3x^2-6x-7=-8x+5

Solution for 3x^2-6x-7=-8x+5 equation:

3x^2-6x-7=-8x+5

We move all terms to the left:

3x^2-6x-7-(-8x+5)=0

We get rid of parentheses

3x^2-6x+8x-5-7=0

We add all the numbers together, and all the variables

3x^2+2x-12=0

a = 3; b = 2; c = -12;
Δ = b2-4ac
Δ = 22-4·3·(-12)
Δ = 148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{37}}{2*3}=\frac{-2-2\sqrt{37}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{37}}{2*3}=\frac{-2+2\sqrt{37}}{6}
$