26x=24-5x^2

Solution for 26x=24-5x^2 equation:

26x=24-5x^2

We move all terms to the left:

26x-(24-5x^2)=0

We get rid of parentheses

5x^2+26x-24=0

a = 5; b = 26; c = -24;
Δ = b2-4ac
Δ = 262-4·5·(-24)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-34}{2*5}=\frac{-60}{10}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+34}{2*5}=\frac{8}{10}
=4/5
$