6x(x+5)=126

Solution for 6x(x+5)=126 equation:

6x(x+5)=126

We move all terms to the left:

6x(x+5)-(126)=0

We multiply parentheses

6x^2+30x-126=0

a = 6; b = 30; c = -126;
Δ = b2-4ac
Δ = 302-4·6·(-126)
Δ = 3924
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:

$\sqrt{\Delta}=\sqrt{3924}=\sqrt{36*109}=\sqrt{36}*\sqrt{109}=6\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{109}}{2*6}=\frac{-30-6\sqrt{109}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{109}}{2*6}=\frac{-30+6\sqrt{109}}{12}
$