10x+2(x-6)=3(4x-4)5x+3(x-3)=6x-11+2x

Solution for 10x+2(x-6)=3(4x-4)5x+3(x-3)=6x-11+2x equation:

10x+2(x-6)=3(4x-4)5x+3(x-3)=6x-11+2x

We move all terms to the left:

10x+2(x-6)-(3(4x-4)5x+3(x-3))=0

We multiply parentheses

10x+2x-(3(4x-4)5x+3(x-3))-12=0


We calculate terms in parentheses: -(3(4x-4)5x+3(x-3)), so:

3(4x-4)5x+3(x-3)

We multiply parentheses

60x^2-60x+3x-9

We add all the numbers together, and all the variables

60x^2-57x-9

Back to the equation:

-(60x^2-57x-9)


We add all the numbers together, and all the variables

12x-(60x^2-57x-9)-12=0

We get rid of parentheses

-60x^2+12x+57x+9-12=0

We add all the numbers together, and all the variables

-60x^2+69x-3=0

a = -60; b = 69; c = -3;
Δ = b2-4ac
Δ = 692-4·(-60)·(-3)
Δ = 4041
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:

$\sqrt{\Delta}=\sqrt{4041}=\sqrt{9*449}=\sqrt{9}*\sqrt{449}=3\sqrt{449}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-3\sqrt{449}}{2*-60}=\frac{-69-3\sqrt{449}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+3\sqrt{449}}{2*-60}=\frac{-69+3\sqrt{449}}{-120}
$