5x(3x+6)=15

Solution for 5x(3x+6)=15 equation:

5x(3x+6)=15

We move all terms to the left:

5x(3x+6)-(15)=0

We multiply parentheses

15x^2+30x-15=0

a = 15; b = 30; c = -15;
Δ = b2-4ac
Δ = 302-4·15·(-15)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30\sqrt{2}}{2*15}=\frac{-30-30\sqrt{2}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30\sqrt{2}}{2*15}=\frac{-30+30\sqrt{2}}{30}
$