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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -((2x+6)5x), so:

(2x+6)5x

We multiply parentheses

10x^2+30x

Back to the equation:

-(10x^2+30x)


We get rid of parentheses

-10x^2+8x-30x-11=0

We add all the numbers together, and all the variables

-10x^2-22x-11=0

a = -10; b = -22; c = -11;
Δ = b2-4ac
Δ = -222-4·(-10)·(-11)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{11}}{2*-10}=\frac{22-2\sqrt{11}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{11}}{2*-10}=\frac{22+2\sqrt{11}}{-20}
$