3x(2x+5)=15

Solution for 3x(2x+5)=15 equation:

3x(2x+5)=15

We move all terms to the left:

3x(2x+5)-(15)=0

We multiply parentheses

6x^2+15x-15=0

a = 6; b = 15; c = -15;
Δ = b2-4ac
Δ = 152-4·6·(-15)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{65}}{2*6}=\frac{-15-3\sqrt{65}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{65}}{2*6}=\frac{-15+3\sqrt{65}}{12}
$