85x-0.5x^2-45x+300=25

Solution for 85x-0.5x^2-45x+300=25 equation:

85x-0.5x^2-45x+300=25

We move all terms to the left:

85x-0.5x^2-45x+300-(25)=0

We add all the numbers together, and all the variables

-0.5x^2+40x+275=0

a = -0.5; b = 40; c = +275;
Δ = b2-4ac
Δ = 402-4·(-0.5)·275
Δ = 2150
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:

$\sqrt{\Delta}=\sqrt{2150}=\sqrt{25*86}=\sqrt{25}*\sqrt{86}=5\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-5\sqrt{86}}{2*-0.5}=\frac{-40-5\sqrt{86}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+5\sqrt{86}}{2*-0.5}=\frac{-40+5\sqrt{86}}{-1}
$