5x(2x+3)=15+20

Solution for 5x(2x+3)=15+20 equation:

5x(2x+3)=15+20

We move all terms to the left:

5x(2x+3)-(15+20)=0

We add all the numbers together, and all the variables

5x(2x+3)-35=0

We multiply parentheses

10x^2+15x-35=0

a = 10; b = 15; c = -35;
Δ = b2-4ac
Δ = 152-4·10·(-35)
Δ = 1625
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:

$\sqrt{\Delta}=\sqrt{1625}=\sqrt{25*65}=\sqrt{25}*\sqrt{65}=5\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{65}}{2*10}=\frac{-15-5\sqrt{65}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{65}}{2*10}=\frac{-15+5\sqrt{65}}{20}
$