x=10x^2-3x-4

Solution for x=10x^2-3x-4 equation:

x=10x^2-3x-4

We move all terms to the left:

x-(10x^2-3x-4)=0

We get rid of parentheses

-10x^2+x+3x+4=0

We add all the numbers together, and all the variables

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

a = -10; b = 4; c = +4;
Δ = b2-4ac
Δ = 42-4·(-10)·4
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{11}}{2*-10}=\frac{-4-4\sqrt{11}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{11}}{2*-10}=\frac{-4+4\sqrt{11}}{-20}
$