(40x-2.5x^2)=90

Solution for (40x-2.5x^2)=90 equation:

(40x-2.5x^2)=90

We move all terms to the left:

(40x-2.5x^2)-(90)=0

We get rid of parentheses

-2.5x^2+40x-90=0

a = -2.5; b = 40; c = -90;
Δ = b2-4ac
Δ = 402-4·(-2.5)·(-90)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10\sqrt{7}}{2*-2.5}=\frac{-40-10\sqrt{7}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10\sqrt{7}}{2*-2.5}=\frac{-40+10\sqrt{7}}{-5}
$