x=4x^2+7x-6

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

x=4x^2+7x-6

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -4; b = -6; c = +6;
Δ = b2-4ac
Δ = -62-4·(-4)·6
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{33}}{2*-4}=\frac{6-2\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{33}}{2*-4}=\frac{6+2\sqrt{33}}{-8}
$