5x(x-6)+8-2x=x+2(x-11)

Solution for 5x(x-6)+8-2x=x+2(x-11) equation:

5x(x-6)+8-2x=x+2(x-11)

We move all terms to the left:

5x(x-6)+8-2x-(x+2(x-11))=0

We add all the numbers together, and all the variables

-2x+5x(x-6)-(x+2(x-11))+8=0

We multiply parentheses

5x^2-2x-30x-(x+2(x-11))+8=0


We calculate terms in parentheses: -(x+2(x-11)), so:

x+2(x-11)

We multiply parentheses

x+2x-22

We add all the numbers together, and all the variables

3x-22

Back to the equation:

-(3x-22)


We add all the numbers together, and all the variables

5x^2-32x-(3x-22)+8=0

We get rid of parentheses

5x^2-32x-3x+22+8=0

We add all the numbers together, and all the variables

5x^2-35x+30=0

a = 5; b = -35; c = +30;
Δ = b2-4ac
Δ = -352-4·5·30
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-25}{2*5}=\frac{10}{10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+25}{2*5}=\frac{60}{10}
=6
$