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

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

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

We move all terms to the left:

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

We multiply parentheses

5x-(2*(x+1)-5x*(x-3))-15=0


We calculate terms in parentheses: -(2*(x+1)-5x*(x-3)), so:

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

We multiply parentheses

-5x^2+2x+15x+2

We add all the numbers together, and all the variables

-5x^2+17x+2

Back to the equation:

-(-5x^2+17x+2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2-12x-17=0

a = 5; b = -12; c = -17;
Δ = b2-4ac
Δ = -122-4·5·(-17)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-22}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+22}{2*5}=\frac{34}{10}
=3+2/5
$