X(3x+8)=100

Solution for X(3x+8)=100 equation:

X(3X+8)=100

We move all terms to the left:

X(3X+8)-(100)=0

We multiply parentheses

3X^2+8X-100=0

a = 3; b = 8; c = -100;
Δ = b2-4ac
Δ = 82-4·3·(-100)
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{79}}{2*3}=\frac{-8-4\sqrt{79}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{79}}{2*3}=\frac{-8+4\sqrt{79}}{6}
$