3x(x-1)+x(5-2x)=0

Solution for 3x(x-1)+x(5-2x)=0 equation:

3x(x-1)+x(5-2x)=0

We add all the numbers together, and all the variables

3x(x-1)+x(-2x+5)=0

We multiply parentheses

3x^2-2x^2-3x+5x=0

We add all the numbers together, and all the variables

x^2+2x=0

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

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*1}=\frac{0}{2}
=0
$