8a(15-a)=6(a-7)+15

Solution for 8a(15-a)=6(a-7)+15 equation:

8a(15-a)=6(a-7)+15

We move all terms to the left:

8a(15-a)-(6(a-7)+15)=0

We add all the numbers together, and all the variables

8a(-1a+15)-(6(a-7)+15)=0

We multiply parentheses

-8a^2+120a-(6(a-7)+15)=0


We calculate terms in parentheses: -(6(a-7)+15), so:

6(a-7)+15

We multiply parentheses

6a-42+15

We add all the numbers together, and all the variables

6a-27

Back to the equation:

-(6a-27)


We get rid of parentheses

-8a^2+120a-6a+27=0

We add all the numbers together, and all the variables

-8a^2+114a+27=0

a = -8; b = 114; c = +27;
Δ = b2-4ac
Δ = 1142-4·(-8)·27
Δ = 13860
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:

$\sqrt{\Delta}=\sqrt{13860}=\sqrt{36*385}=\sqrt{36}*\sqrt{385}=6\sqrt{385}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-6\sqrt{385}}{2*-8}=\frac{-114-6\sqrt{385}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+6\sqrt{385}}{2*-8}=\frac{-114+6\sqrt{385}}{-16}
$