6x-4=2x^2-10x-7

Solution for 6x-4=2x^2-10x-7 equation:

6x-4=2x^2-10x-7

We move all terms to the left:

6x-4-(2x^2-10x-7)=0

We get rid of parentheses

-2x^2+6x+10x+7-4=0

We add all the numbers together, and all the variables

-2x^2+16x+3=0

a = -2; b = 16; c = +3;
Δ = b2-4ac
Δ = 162-4·(-2)·3
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{70}}{2*-2}=\frac{-16-2\sqrt{70}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{70}}{2*-2}=\frac{-16+2\sqrt{70}}{-4}
$