4x^2-2x-74=0

Solution for 4x^2-2x-74=0 equation:

4x^2-2x-74=0

a = 4; b = -2; c = -74;
Δ = b2-4ac
Δ = -22-4·4·(-74)
Δ = 1188
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:

$\sqrt{\Delta}=\sqrt{1188}=\sqrt{36*33}=\sqrt{36}*\sqrt{33}=6\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{33}}{2*4}=\frac{2-6\sqrt{33}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{33}}{2*4}=\frac{2+6\sqrt{33}}{8}
$