5x(3x+2)=39

Solution for 5x(3x+2)=39 equation:

5x(3x+2)=39

We move all terms to the left:

5x(3x+2)-(39)=0

We multiply parentheses

15x^2+10x-39=0

a = 15; b = 10; c = -39;
Δ = b2-4ac
Δ = 102-4·15·(-39)
Δ = 2440
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:

$\sqrt{\Delta}=\sqrt{2440}=\sqrt{4*610}=\sqrt{4}*\sqrt{610}=2\sqrt{610}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{610}}{2*15}=\frac{-10-2\sqrt{610}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{610}}{2*15}=\frac{-10+2\sqrt{610}}{30}
$