4x^2-38.65x+92.16=0

Solution for 4x^2-38.65x+92.16=0 equation:

4x^2-38.65x+92.16=0

a = 4; b = -38.65; c = +92.16;
Δ = b2-4ac
Δ = -38.652-4·4·92.16
Δ = 19.2625
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{-(-38.65)-\sqrt{19.2625}}{2*4}=\frac{38.65-\sqrt{19.2625}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38.65)+\sqrt{19.2625}}{2*4}=\frac{38.65+\sqrt{19.2625}}{8}
$