-x^2=14x-24

Solution for -x^2=14x-24 equation:

-x^2=14x-24

We move all terms to the left:

-x^2-(14x-24)=0

We add all the numbers together, and all the variables

-1x^2-(14x-24)=0

We get rid of parentheses

-1x^2-14x+24=0

a = -1; b = -14; c = +24;
Δ = b2-4ac
Δ = -142-4·(-1)·24
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{73}}{2*-1}=\frac{14-2\sqrt{73}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{73}}{2*-1}=\frac{14+2\sqrt{73}}{-2}
$