8x+11x(x-5)=-11(3x-5)-6

Solution for 8x+11x(x-5)=-11(3x-5)-6 equation:

8x+11x(x-5)=-11(3x-5)-6

We move all terms to the left:

8x+11x(x-5)-(-11(3x-5)-6)=0

We multiply parentheses

11x^2+8x-55x-(-11(3x-5)-6)=0


We calculate terms in parentheses: -(-11(3x-5)-6), so:

-11(3x-5)-6

We multiply parentheses

-33x+55-6

We add all the numbers together, and all the variables

-33x+49

Back to the equation:

-(-33x+49)


We add all the numbers together, and all the variables

11x^2-47x-(-33x+49)=0

We get rid of parentheses

11x^2-47x+33x-49=0

We add all the numbers together, and all the variables

11x^2-14x-49=0

a = 11; b = -14; c = -49;
Δ = b2-4ac
Δ = -142-4·11·(-49)
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-28\sqrt{3}}{2*11}=\frac{14-28\sqrt{3}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+28\sqrt{3}}{2*11}=\frac{14+28\sqrt{3}}{22}
$