5x(2-x)=3x

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

5x(2-x)=3x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-5x^2-3x+10x=0

We add all the numbers together, and all the variables

-5x^2+7x=0

a = -5; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-5)·0
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{-(7)-7}{2*-5}=\frac{-14}{-10}
=1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-5}=\frac{0}{-10}
=0
$