5a^2=-7a+24

Solution for 5a^2=-7a+24 equation:

5a^2=-7a+24

We move all terms to the left:

5a^2-(-7a+24)=0

We get rid of parentheses

5a^2+7a-24=0

a = 5; b = 7; c = -24;
Δ = b2-4ac
Δ = 72-4·5·(-24)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-23}{2*5}=\frac{-30}{10}
=-3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+23}{2*5}=\frac{16}{10}
=1+3/5
$