2x(3x+2)=100

Solution for 2x(3x+2)=100 equation:

2x(3x+2)=100

We move all terms to the left:

2x(3x+2)-(100)=0

We multiply parentheses

6x^2+4x-100=0

a = 6; b = 4; c = -100;
Δ = b2-4ac
Δ = 42-4·6·(-100)
Δ = 2416
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:

$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{151}}{2*6}=\frac{-4-4\sqrt{151}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{151}}{2*6}=\frac{-4+4\sqrt{151}}{12}
$