4x^2-32x-34=0

Solution for 4x^2-32x-34=0 equation:

4x^2-32x-34=0

a = 4; b = -32; c = -34;
Δ = b2-4ac
Δ = -322-4·4·(-34)
Δ = 1568
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:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-28\sqrt{2}}{2*4}=\frac{32-28\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+28\sqrt{2}}{2*4}=\frac{32+28\sqrt{2}}{8}
$