-4x^2+54x-173=0

Solution for -4x^2+54x-173=0 equation:

-4x^2+54x-173=0

a = -4; b = 54; c = -173;
Δ = b2-4ac
Δ = 542-4·(-4)·(-173)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{37}}{2*-4}=\frac{-54-2\sqrt{37}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{37}}{2*-4}=\frac{-54+2\sqrt{37}}{-8}
$