2x(x+3)=15

Solution for 2x(x+3)=15 equation:

2x(x+3)=15

We move all terms to the left:

2x(x+3)-(15)=0

We multiply parentheses

2x^2+6x-15=0

a = 2; b = 6; c = -15;
Δ = b2-4ac
Δ = 62-4·2·(-15)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{39}}{2*2}=\frac{-6-2\sqrt{39}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{39}}{2*2}=\frac{-6+2\sqrt{39}}{4}
$