4x^2-35x+58=0

Solution for 4x^2-35x+58=0 equation:

4x^2-35x+58=0

a = 4; b = -35; c = +58;
Δ = b2-4ac
Δ = -352-4·4·58
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-3\sqrt{33}}{2*4}=\frac{35-3\sqrt{33}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+3\sqrt{33}}{2*4}=\frac{35+3\sqrt{33}}{8}
$