6x^2+52x+34=0

Solution for 6x^2+52x+34=0 equation:

6x^2+52x+34=0

a = 6; b = 52; c = +34;
Δ = b2-4ac
Δ = 522-4·6·34
Δ = 1888
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:

$\sqrt{\Delta}=\sqrt{1888}=\sqrt{16*118}=\sqrt{16}*\sqrt{118}=4\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{118}}{2*6}=\frac{-52-4\sqrt{118}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{118}}{2*6}=\frac{-52+4\sqrt{118}}{12}
$