-2x^2+20x=47

Solution for -2x^2+20x=47 equation:

-2x^2+20x=47

We move all terms to the left:

-2x^2+20x-(47)=0

a = -2; b = 20; c = -47;
Δ = b2-4ac
Δ = 202-4·(-2)·(-47)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{6}}{2*-2}=\frac{-20-2\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{6}}{2*-2}=\frac{-20+2\sqrt{6}}{-4}
$