x(2x-3)-3(5-x)=2(x-9)+3*1

Solution for x(2x-3)-3(5-x)=2(x-9)+3*1 equation:

x(2x-3)-3(5-x)=2(x-9)+3*1

We move all terms to the left:

x(2x-3)-3(5-x)-(2(x-9)+3*1)=0

We add all the numbers together, and all the variables

x(2x-3)-3(-1x+5)-(2(x-9)+3*1)=0

We multiply parentheses

2x^2-3x+3x-(2(x-9)+3*1)-15=0


We calculate terms in parentheses: -(2(x-9)+3*1), so:

2(x-9)+3*1

We add all the numbers together, and all the variables

2(x-9)+3

We multiply parentheses

2x-18+3

We add all the numbers together, and all the variables

2x-15

Back to the equation:

-(2x-15)


We add all the numbers together, and all the variables

2x^2-(2x-15)-15=0

We get rid of parentheses

2x^2-2x+15-15=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
$