-7x^2-54x+34=0

Solution for -7x^2-54x+34=0 equation:

-7x^2-54x+34=0

a = -7; b = -54; c = +34;
Δ = b2-4ac
Δ = -542-4·(-7)·34
Δ = 3868
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:

$\sqrt{\Delta}=\sqrt{3868}=\sqrt{4*967}=\sqrt{4}*\sqrt{967}=2\sqrt{967}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{967}}{2*-7}=\frac{54-2\sqrt{967}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{967}}{2*-7}=\frac{54+2\sqrt{967}}{-14}
$