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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -((8x-11)), so:

(8x-11)

We get rid of parentheses

8x-11

Back to the equation:

-(8x-11)


We get rid of parentheses

10x^2+30x-8x+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}
$