362=-6+8(7a-3)a=

Solution for 362=-6+8(7a-3)a= equation:

362=-6+8(7a-3)a=

We move all terms to the left:

362-(-6+8(7a-3)a)=0


We calculate terms in parentheses: -(-6+8(7a-3)a), so:

-6+8(7a-3)a

determiningTheFunctionDomain
8(7a-3)a-6

We multiply parentheses

56a^2-24a-6

Back to the equation:

-(56a^2-24a-6)


We get rid of parentheses

-56a^2+24a+6+362=0

We add all the numbers together, and all the variables

-56a^2+24a+368=0

a = -56; b = 24; c = +368;
Δ = b2-4ac
Δ = 242-4·(-56)·368
Δ = 83008
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:

$\sqrt{\Delta}=\sqrt{83008}=\sqrt{64*1297}=\sqrt{64}*\sqrt{1297}=8\sqrt{1297}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{1297}}{2*-56}=\frac{-24-8\sqrt{1297}}{-112}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{1297}}{2*-56}=\frac{-24+8\sqrt{1297}}{-112}
$