1040+14x-x^2=0

Solution for 1040+14x-x^2=0 equation:

1040+14x-x^2=0

We add all the numbers together, and all the variables

-1x^2+14x+1040=0

a = -1; b = 14; c = +1040;
Δ = b2-4ac
Δ = 142-4·(-1)·1040
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-66}{2*-1}=\frac{-80}{-2}
=+40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+66}{2*-1}=\frac{52}{-2}
=-26
$