24+5x-x2=-3

Solution for 24+5x-x2=-3 equation:

24+5x-x2=-3

We move all terms to the left:

24+5x-x2-(-3)=0

We add all the numbers together, and all the variables

-1x^2+5x+27=0

a = -1; b = 5; c = +27;
Δ = b2-4ac
Δ = 52-4·(-1)·27
Δ = 133
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{133}}{2*-1}=\frac{-5-\sqrt{133}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{133}}{2*-1}=\frac{-5+\sqrt{133}}{-2}
$