14x^2-36x-3=0

Solution for 14x^2-36x-3=0 equation:

14x^2-36x-3=0

a = 14; b = -36; c = -3;
Δ = b2-4ac
Δ = -362-4·14·(-3)
Δ = 1464
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:

$\sqrt{\Delta}=\sqrt{1464}=\sqrt{4*366}=\sqrt{4}*\sqrt{366}=2\sqrt{366}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{366}}{2*14}=\frac{36-2\sqrt{366}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{366}}{2*14}=\frac{36+2\sqrt{366}}{28}
$