4x^2-12x-74=0

Solution for 4x^2-12x-74=0 equation:

4x^2-12x-74=0

a = 4; b = -12; c = -74;
Δ = b2-4ac
Δ = -122-4·4·(-74)
Δ = 1328
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:

$\sqrt{\Delta}=\sqrt{1328}=\sqrt{16*83}=\sqrt{16}*\sqrt{83}=4\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{83}}{2*4}=\frac{12-4\sqrt{83}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{83}}{2*4}=\frac{12+4\sqrt{83}}{8}
$