34x^2-65x+21=0

Solution for 34x^2-65x+21=0 equation:

34x^2-65x+21=0

a = 34; b = -65; c = +21;
Δ = b2-4ac
Δ = -652-4·34·21
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-37}{2*34}=\frac{28}{68}
=7/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+37}{2*34}=\frac{102}{68}
=1+1/2
$