5x(-3x-7)=0

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

5x(-3x-7)=0

We multiply parentheses

-15x^2-35x=0

a = -15; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·(-15)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*-15}=\frac{70}{-30}
=-2+1/3
$