14x^2-234x+634=0

Solution for 14x^2-234x+634=0 equation:

14x^2-234x+634=0

a = 14; b = -234; c = +634;
Δ = b2-4ac
Δ = -2342-4·14·634
Δ = 19252
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:

$\sqrt{\Delta}=\sqrt{19252}=\sqrt{4*4813}=\sqrt{4}*\sqrt{4813}=2\sqrt{4813}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-234)-2\sqrt{4813}}{2*14}=\frac{234-2\sqrt{4813}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-234)+2\sqrt{4813}}{2*14}=\frac{234+2\sqrt{4813}}{28}
$