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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(2x-(-1x+5)x), so:

2x-(-1x+5)x

We multiply parentheses

1x^2+2x-5x

We add all the numbers together, and all the variables

x^2-3x

Back to the equation:

-(x^2-3x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-2x=0

a = 2; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·2·0
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*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*2}=\frac{4}{4}
=1
$