4x^2-14x-7=0

Solution for 4x^2-14x-7=0 equation:

4x^2-14x-7=0

a = 4; b = -14; c = -7;
Δ = b2-4ac
Δ = -142-4·4·(-7)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{77}}{2*4}=\frac{14-2\sqrt{77}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{77}}{2*4}=\frac{14+2\sqrt{77}}{8}
$