5a^2=8a+85

Solution for 5a^2=8a+85 equation:

5a^2=8a+85

We move all terms to the left:

5a^2-(8a+85)=0

We get rid of parentheses

5a^2-8a-85=0

a = 5; b = -8; c = -85;
Δ = b2-4ac
Δ = -82-4·5·(-85)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-42}{2*5}=\frac{-34}{10}
=-3+2/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+42}{2*5}=\frac{50}{10}
=5
$