-x^2+15x-20=3x-44

Solution for -x^2+15x-20=3x-44 equation:

-x^2+15x-20=3x-44

We move all terms to the left:

-x^2+15x-20-(3x-44)=0

We add all the numbers together, and all the variables

-1x^2+15x-(3x-44)-20=0

We get rid of parentheses

-1x^2+15x-3x+44-20=0

We add all the numbers together, and all the variables

-1x^2+12x+24=0

a = -1; b = 12; c = +24;
Δ = b2-4ac
Δ = 122-4·(-1)·24
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{15}}{2*-1}=\frac{-12-4\sqrt{15}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{15}}{2*-1}=\frac{-12+4\sqrt{15}}{-2}
$