14x^2+58x-16=0

Solution for 14x^2+58x-16=0 equation:

14x^2+58x-16=0

a = 14; b = 58; c = -16;
Δ = b2-4ac
Δ = 582-4·14·(-16)
Δ = 4260
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:

$\sqrt{\Delta}=\sqrt{4260}=\sqrt{4*1065}=\sqrt{4}*\sqrt{1065}=2\sqrt{1065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-2\sqrt{1065}}{2*14}=\frac{-58-2\sqrt{1065}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+2\sqrt{1065}}{2*14}=\frac{-58+2\sqrt{1065}}{28}
$