95.5=4x2+37x+40

Solution for 95.5=4x2+37x+40 equation:

95.5=4x^2+37x+40

We move all terms to the left:

95.5-(4x^2+37x+40)=0

We get rid of parentheses

-4x^2-37x-40+95.5=0

We add all the numbers together, and all the variables

-4x^2-37x+55.5=0

a = -4; b = -37; c = +55.5;
Δ = b2-4ac
Δ = -372-4·(-4)·55.5
Δ = 2257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{2257}}{2*-4}=\frac{37-\sqrt{2257}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{2257}}{2*-4}=\frac{37+\sqrt{2257}}{-8}
$