-16x^2+80x=84

Solution for -16x^2+80x=84 equation:

-16x^2+80x=84

We move all terms to the left:

-16x^2+80x-(84)=0

a = -16; b = 80; c = -84;
Δ = b2-4ac
Δ = 802-4·(-16)·(-84)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-32}{2*-16}=\frac{-112}{-32}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+32}{2*-16}=\frac{-48}{-32}
=1+1/2
$