3x(1+x)=90

Solution for 3x(1+x)=90 equation:

3x(1+x)=90

We move all terms to the left:

3x(1+x)-(90)=0

We add all the numbers together, and all the variables

3x(x+1)-90=0

We multiply parentheses

3x^2+3x-90=0

a = 3; b = 3; c = -90;
Δ = b2-4ac
Δ = 32-4·3·(-90)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-33}{2*3}=\frac{-36}{6}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+33}{2*3}=\frac{30}{6}
=5
$