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

Wy multiply elements

152a-((8a-6)(a+5))=0

We multiply parentheses ..

-((+8a^2+40a-6a-30))+152a=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

152a-(8a^2+34a-30)=0

We get rid of parentheses

-8a^2+152a-34a+30=0

We add all the numbers together, and all the variables

-8a^2+118a+30=0

a = -8; b = 118; c = +30;
Δ = b2-4ac
Δ = 1182-4·(-8)·30
Δ = 14884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14884}=122$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(118)-122}{2*-8}=\frac{-240}{-16}
=+15
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(118)+122}{2*-8}=\frac{4}{-16}
=-1/4
$