x=4x^2-7x-2

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

x=4x^2-7x-2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4x^2+8x+2=0

a = -4; b = 8; c = +2;
Δ = b2-4ac
Δ = 82-4·(-4)·2
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*-4}=\frac{-8-4\sqrt{6}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*-4}=\frac{-8+4\sqrt{6}}{-8}
$