190x-x^2=7000

Solution for 190x-x^2=7000 equation:

190x-x^2=7000

We move all terms to the left:

190x-x^2-(7000)=0

We add all the numbers together, and all the variables

-1x^2+190x-7000=0

a = -1; b = 190; c = -7000;
Δ = b2-4ac
Δ = 1902-4·(-1)·(-7000)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(190)-90}{2*-1}=\frac{-280}{-2}
=+140
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(190)+90}{2*-1}=\frac{-100}{-2}
=+50
$