x=4x^2+24x-10

Solution for x=4x^2+24x-10 equation:

x=4x^2+24x-10

We move all terms to the left:

x-(4x^2+24x-10)=0

We get rid of parentheses

-4x^2+x-24x+10=0

We add all the numbers together, and all the variables

-4x^2-23x+10=0

a = -4; b = -23; c = +10;
Δ = b2-4ac
Δ = -232-4·(-4)·10
Δ = 689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{689}}{2*-4}=\frac{23-\sqrt{689}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{689}}{2*-4}=\frac{23+\sqrt{689}}{-8}
$