5a^2-37a=24

Solution for 5a^2-37a=24 equation:

5a^2-37a=24

We move all terms to the left:

5a^2-37a-(24)=0

a = 5; b = -37; c = -24;
Δ = b2-4ac
Δ = -372-4·5·(-24)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-43}{2*5}=\frac{-6}{10}
=-3/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+43}{2*5}=\frac{80}{10}
=8
$