4x^2-12x-58=0

Solution for 4x^2-12x-58=0 equation:

4x^2-12x-58=0

a = 4; b = -12; c = -58;
Δ = b2-4ac
Δ = -122-4·4·(-58)
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{67}}{2*4}=\frac{12-4\sqrt{67}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{67}}{2*4}=\frac{12+4\sqrt{67}}{8}
$