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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

5x+6x-(5x(-1x+3))-6=0


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

5x(-1x+3)

We multiply parentheses

-5x^2+15x

Back to the equation:

-(-5x^2+15x)


We add all the numbers together, and all the variables

-(-5x^2+15x)+11x-6=0

We get rid of parentheses

5x^2-15x+11x-6=0

We add all the numbers together, and all the variables

5x^2-4x-6=0

a = 5; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·5·(-6)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{34}}{2*5}=\frac{4-2\sqrt{34}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{34}}{2*5}=\frac{4+2\sqrt{34}}{10}
$