64=5x^2+30x+24

Solution for 64=5x^2+30x+24 equation:

64=5x^2+30x+24

We move all terms to the left:

64-(5x^2+30x+24)=0

We get rid of parentheses

-5x^2-30x-24+64=0

We add all the numbers together, and all the variables

-5x^2-30x+40=0

a = -5; b = -30; c = +40;
Δ = b2-4ac
Δ = -302-4·(-5)·40
Δ = 1700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{17}}{2*-5}=\frac{30-10\sqrt{17}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{17}}{2*-5}=\frac{30+10\sqrt{17}}{-10}
$