x=2x^2-3x-35

Solution for x=2x^2-3x-35 equation:

x=2x^2-3x-35

We move all terms to the left:

x-(2x^2-3x-35)=0

We get rid of parentheses

-2x^2+x+3x+35=0

We add all the numbers together, and all the variables

-2x^2+4x+35=0

a = -2; b = 4; c = +35;
Δ = b2-4ac
Δ = 42-4·(-2)·35
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{74}}{2*-2}=\frac{-4-2\sqrt{74}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{74}}{2*-2}=\frac{-4+2\sqrt{74}}{-4}
$