3x(5x+2)=90

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

3x(5x+2)=90

We move all terms to the left:

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

We multiply parentheses

15x^2+6x-90=0

a = 15; b = 6; c = -90;
Δ = b2-4ac
Δ = 62-4·15·(-90)
Δ = 5436
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:

$\sqrt{\Delta}=\sqrt{5436}=\sqrt{36*151}=\sqrt{36}*\sqrt{151}=6\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{151}}{2*15}=\frac{-6-6\sqrt{151}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{151}}{2*15}=\frac{-6+6\sqrt{151}}{30}
$