8x^2-34x-9=5

Solution for 8x^2-34x-9=5 equation:

8x^2-34x-9=5

We move all terms to the left:

8x^2-34x-9-(5)=0

We add all the numbers together, and all the variables

8x^2-34x-14=0

a = 8; b = -34; c = -14;
Δ = b2-4ac
Δ = -342-4·8·(-14)
Δ = 1604
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:

$\sqrt{\Delta}=\sqrt{1604}=\sqrt{4*401}=\sqrt{4}*\sqrt{401}=2\sqrt{401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{401}}{2*8}=\frac{34-2\sqrt{401}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{401}}{2*8}=\frac{34+2\sqrt{401}}{16}
$