76+2a=(8a-6)(a+5)

Solution for 76+2a=(8a-6)(a+5) equation:

76+2a=(8a-6)(a+5)

We move all terms to the left:

76+2a-((8a-6)(a+5))=0

We multiply parentheses ..

-((+8a^2+40a-6a-30))+2a+76=0


We calculate terms in parentheses: -((+8a^2+40a-6a-30)), so:

(+8a^2+40a-6a-30)

We get rid of parentheses

8a^2+40a-6a-30

We add all the numbers together, and all the variables

8a^2+34a-30

Back to the equation:

-(8a^2+34a-30)


We add all the numbers together, and all the variables

2a-(8a^2+34a-30)+76=0

We get rid of parentheses

-8a^2+2a-34a+30+76=0

We add all the numbers together, and all the variables

-8a^2-32a+106=0

a = -8; b = -32; c = +106;
Δ = b2-4ac
Δ = -322-4·(-8)·106
Δ = 4416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{69}}{2*-8}=\frac{32-8\sqrt{69}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{69}}{2*-8}=\frac{32+8\sqrt{69}}{-16}
$