10x(15x+30)=90

Solution for 10x(15x+30)=90 equation:

10x(15x+30)=90

We move all terms to the left:

10x(15x+30)-(90)=0

We multiply parentheses

150x^2+300x-90=0

a = 150; b = 300; c = -90;
Δ = b2-4ac
Δ = 3002-4·150·(-90)
Δ = 144000
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:

$\sqrt{\Delta}=\sqrt{144000}=\sqrt{14400*10}=\sqrt{14400}*\sqrt{10}=120\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-120\sqrt{10}}{2*150}=\frac{-300-120\sqrt{10}}{300}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+120\sqrt{10}}{2*150}=\frac{-300+120\sqrt{10}}{300}
$