5a^2+6a-24=0

Solution for 5a^2+6a-24=0 equation:

5a^2+6a-24=0

a = 5; b = 6; c = -24;
Δ = b2-4ac
Δ = 62-4·5·(-24)
Δ = 516
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{129}}{2*5}=\frac{-6-2\sqrt{129}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{129}}{2*5}=\frac{-6+2\sqrt{129}}{10}
$