15a+1/24-12a^2+23a=0

Solution for 15a+1/24-12a^2+23a=0 equation:

15a+1/24-12a^2+23a=0

We add all the numbers together, and all the variables

-12a^2+38a+1/24=0

We multiply all the terms by the denominator


-12a^2*24+38a*24+1=0

Wy multiply elements

-288a^2+912a+1=0

a = -288; b = 912; c = +1;
Δ = b2-4ac
Δ = 9122-4·(-288)·1
Δ = 832896
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:

$\sqrt{\Delta}=\sqrt{832896}=\sqrt{576*1446}=\sqrt{576}*\sqrt{1446}=24\sqrt{1446}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(912)-24\sqrt{1446}}{2*-288}=\frac{-912-24\sqrt{1446}}{-576}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(912)+24\sqrt{1446}}{2*-288}=\frac{-912+24\sqrt{1446}}{-576}
$