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

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

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

We move all terms to the left:

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

We multiply parentheses

5x^2+30x-(-2(x-8))+6=0


We calculate terms in parentheses: -(-2(x-8)), so:

-2(x-8)

We multiply parentheses

-2x+16

Back to the equation:

-(-2x+16)


We get rid of parentheses

5x^2+30x+2x-16+6=0

We add all the numbers together, and all the variables

5x^2+32x-10=0

a = 5; b = 32; c = -10;
Δ = b2-4ac
Δ = 322-4·5·(-10)
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-6\sqrt{34}}{2*5}=\frac{-32-6\sqrt{34}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+6\sqrt{34}}{2*5}=\frac{-32+6\sqrt{34}}{10}
$