7x+3x(x+5)=0

Solution for 7x+3x(x+5)=0 equation:

7x+3x(x+5)=0

We multiply parentheses

3x^2+7x+15x=0

We add all the numbers together, and all the variables

3x^2+22x=0

a = 3; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·3·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*3}=\frac{-44}{6}
=-7+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*3}=\frac{0}{6}
=0
$