8a^2-34a+21=0

Solution for 8a^2-34a+21=0 equation:

8a^2-34a+21=0

a = 8; b = -34; c = +21;
Δ = b2-4ac
Δ = -342-4·8·21
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-22}{2*8}=\frac{12}{16}
=3/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+22}{2*8}=\frac{56}{16}
=3+1/2
$