40x-3x^2=55

Solution for 40x-3x^2=55 equation:

40x-3x^2=55

We move all terms to the left:

40x-3x^2-(55)=0

a = -3; b = 40; c = -55;
Δ = b2-4ac
Δ = 402-4·(-3)·(-55)
Δ = 940
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:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{235}}{2*-3}=\frac{-40-2\sqrt{235}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{235}}{2*-3}=\frac{-40+2\sqrt{235}}{-6}
$