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

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

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

We move all terms to the left:

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


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

3x(x-1)

We multiply parentheses

3x^2-3x

Back to the equation:

-(3x^2-3x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+8x+5=0

a = -3; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·(-3)·5
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{31}}{2*-3}=\frac{-8-2\sqrt{31}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{31}}{2*-3}=\frac{-8+2\sqrt{31}}{-6}
$