21x^2-84x+65=0

Solution for 21x^2-84x+65=0 equation:

21x^2-84x+65=0

a = 21; b = -84; c = +65;
Δ = b2-4ac
Δ = -842-4·21·65
Δ = 1596
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:

$\sqrt{\Delta}=\sqrt{1596}=\sqrt{4*399}=\sqrt{4}*\sqrt{399}=2\sqrt{399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{399}}{2*21}=\frac{84-2\sqrt{399}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{399}}{2*21}=\frac{84+2\sqrt{399}}{42}
$