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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4x^2+11x-1=0

a = -4; b = 11; c = -1;
Δ = b2-4ac
Δ = 112-4·(-4)·(-1)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{105}}{2*-4}=\frac{-11-\sqrt{105}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{105}}{2*-4}=\frac{-11+\sqrt{105}}{-8}
$