5a^2-3a=8

Solution for 5a^2-3a=8 equation:

5a^2-3a=8

We move all terms to the left:

5a^2-3a-(8)=0

a = 5; b = -3; c = -8;
Δ = b2-4ac
Δ = -32-4·5·(-8)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13}{2*5}=\frac{-10}{10}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*5}=\frac{16}{10}
=1+3/5
$