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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

2(x-9)+3x+1

We add all the numbers together, and all the variables

3x+2(x-9)+1

We multiply parentheses

3x+2x-18+1

We add all the numbers together, and all the variables

5x-17

Back to the equation:

-(5x-17)


We add all the numbers together, and all the variables

2x^2-(5x-17)-15=0

We get rid of parentheses

2x^2-5x+17-15=0

We add all the numbers together, and all the variables

2x^2-5x+2=0

a = 2; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·2·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*2}=\frac{2}{4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*2}=\frac{8}{4}
=2
$