(3x)(x+1)=93

Solution for (3x)(x+1)=93 equation:

(3x)(x+1)=93

We move all terms to the left:

(3x)(x+1)-(93)=0

We multiply parentheses

3x^2+3x-93=0

a = 3; b = 3; c = -93;
Δ = b2-4ac
Δ = 32-4·3·(-93)
Δ = 1125
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:

$\sqrt{\Delta}=\sqrt{1125}=\sqrt{225*5}=\sqrt{225}*\sqrt{5}=15\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15\sqrt{5}}{2*3}=\frac{-3-15\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15\sqrt{5}}{2*3}=\frac{-3+15\sqrt{5}}{6}
$