126=x(4x+8)

Solution for 126=x(4x+8) equation:

126=x(4x+8)

We move all terms to the left:

126-(x(4x+8))=0


We calculate terms in parentheses: -(x(4x+8)), so:

x(4x+8)

We multiply parentheses

4x^2+8x

Back to the equation:

-(4x^2+8x)


We get rid of parentheses

-4x^2-8x+126=0

a = -4; b = -8; c = +126;
Δ = b2-4ac
Δ = -82-4·(-4)·126
Δ = 2080
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:

$\sqrt{\Delta}=\sqrt{2080}=\sqrt{16*130}=\sqrt{16}*\sqrt{130}=4\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{130}}{2*-4}=\frac{8-4\sqrt{130}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{130}}{2*-4}=\frac{8+4\sqrt{130}}{-8}
$