8v^2-34v+29=0

Solution for 8v^2-34v+29=0 equation:

8v^2-34v+29=0

a = 8; b = -34; c = +29;
Δ = b2-4ac
Δ = -342-4·8·29
Δ = 228
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{57}}{2*8}=\frac{34-2\sqrt{57}}{16}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{57}}{2*8}=\frac{34+2\sqrt{57}}{16}
$