8q^2-14q+5=0

Solution for 8q^2-14q+5=0 equation:

8q^2-14q+5=0

a = 8; b = -14; c = +5;
Δ = b2-4ac
Δ = -142-4·8·5
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6}{2*8}=\frac{8}{16}
=1/2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6}{2*8}=\frac{20}{16}
=1+1/4
$