-1x^2+38x=280

Solution for -1x^2+38x=280 equation:

-1x^2+38x=280

We move all terms to the left:

-1x^2+38x-(280)=0

a = -1; b = 38; c = -280;
Δ = b2-4ac
Δ = 382-4·(-1)·(-280)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-18}{2*-1}=\frac{-56}{-2}
=+28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+18}{2*-1}=\frac{-20}{-2}
=+10
$