3x(2x+5)=90

Solution for 3x(2x+5)=90 equation:

3x(2x+5)=90

We move all terms to the left:

3x(2x+5)-(90)=0

We multiply parentheses

6x^2+15x-90=0

a = 6; b = 15; c = -90;
Δ = b2-4ac
Δ = 152-4·6·(-90)
Δ = 2385
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:

$\sqrt{\Delta}=\sqrt{2385}=\sqrt{9*265}=\sqrt{9}*\sqrt{265}=3\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{265}}{2*6}=\frac{-15-3\sqrt{265}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{265}}{2*6}=\frac{-15+3\sqrt{265}}{12}
$