4x2+37x+40=95.5

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

4x^2+37x+40=95.5

We move all terms to the left:

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}
$