6x(x+1)=100

Solution for 6x(x+1)=100 equation:

6x(x+1)=100

We move all terms to the left:

6x(x+1)-(100)=0

We multiply parentheses

6x^2+6x-100=0

a = 6; b = 6; c = -100;
Δ = b2-4ac
Δ = 62-4·6·(-100)
Δ = 2436
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:

$\sqrt{\Delta}=\sqrt{2436}=\sqrt{4*609}=\sqrt{4}*\sqrt{609}=2\sqrt{609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{609}}{2*6}=\frac{-6-2\sqrt{609}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{609}}{2*6}=\frac{-6+2\sqrt{609}}{12}
$