(a-8)+7=5(a2)-3a-19

Solution for (a-8)+7=5(a2)-3a-19 equation:

(a-8)+7=5(a2)-3a-19

We move all terms to the left:

(a-8)+7-(5(a2)-3a-19)=0

We add all the numbers together, and all the variables

-(+5a^2-3a-19)+(a-8)+7=0

We get rid of parentheses

-5a^2+3a+a+19-8+7=0

We add all the numbers together, and all the variables

-5a^2+4a+18=0

a = -5; b = 4; c = +18;
Δ = b2-4ac
Δ = 42-4·(-5)·18
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{94}}{2*-5}=\frac{-4-2\sqrt{94}}{-10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{94}}{2*-5}=\frac{-4+2\sqrt{94}}{-10}
$