30x-x^2=140

Solution for 30x-x^2=140 equation:

30x-x^2=140

We move all terms to the left:

30x-x^2-(140)=0

We add all the numbers together, and all the variables

-1x^2+30x-140=0

a = -1; b = 30; c = -140;
Δ = b2-4ac
Δ = 302-4·(-1)·(-140)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{85}}{2*-1}=\frac{-30-2\sqrt{85}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{85}}{2*-1}=\frac{-30+2\sqrt{85}}{-2}
$