4y^2-54y+175=0

Solution for 4y^2-54y+175=0 equation:

4y^2-54y+175=0

a = 4; b = -54; c = +175;
Δ = b2-4ac
Δ = -542-4·4·175
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{29}}{2*4}=\frac{54-2\sqrt{29}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{29}}{2*4}=\frac{54+2\sqrt{29}}{8}
$