-x^2+14x=20

Solution for -x^2+14x=20 equation:

-x^2+14x=20

We move all terms to the left:

-x^2+14x-(20)=0

We add all the numbers together, and all the variables

-1x^2+14x-20=0

a = -1; b = 14; c = -20;
Δ = b2-4ac
Δ = 142-4·(-1)·(-20)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{29}}{2*-1}=\frac{-14-2\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{29}}{2*-1}=\frac{-14+2\sqrt{29}}{-2}
$