8x(x+1)=126

Solution for 8x(x+1)=126 equation:

8x(x+1)=126

We move all terms to the left:

8x(x+1)-(126)=0

We multiply parentheses

8x^2+8x-126=0

a = 8; b = 8; c = -126;
Δ = b2-4ac
Δ = 82-4·8·(-126)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-64}{2*8}=\frac{-72}{16}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+64}{2*8}=\frac{56}{16}
=3+1/2
$