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

Solution for 2x(x+5)+3(x+5)=0 equation:

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

We multiply parentheses

2x^2+10x+3x+15=0

We add all the numbers together, and all the variables

2x^2+13x+15=0

a = 2; b = 13; c = +15;
Δ = b2-4ac
Δ = 132-4·2·15
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-7}{2*2}=\frac{-20}{4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*2}=\frac{-6}{4}
=-1+1/2
$