3x(5x+2)=13

Solution for 3x(5x+2)=13 equation:

3x(5x+2)=13

We move all terms to the left:

3x(5x+2)-(13)=0

We multiply parentheses

15x^2+6x-13=0

a = 15; b = 6; c = -13;
Δ = b2-4ac
Δ = 62-4·15·(-13)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{51}}{2*15}=\frac{-6-4\sqrt{51}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{51}}{2*15}=\frac{-6+4\sqrt{51}}{30}
$