5a^2+36=39a+8

Solution for 5a^2+36=39a+8 equation:

5a^2+36=39a+8

We move all terms to the left:

5a^2+36-(39a+8)=0

We get rid of parentheses

5a^2-39a-8+36=0

We add all the numbers together, and all the variables

5a^2-39a+28=0

a = 5; b = -39; c = +28;
Δ = b2-4ac
Δ = -392-4·5·28
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-31}{2*5}=\frac{8}{10}
=4/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+31}{2*5}=\frac{70}{10}
=7
$