2x^2-5=14x

Solution for 2x^2-5=14x equation:

2x^2-5=14x

We move all terms to the left:

2x^2-5-(14x)=0

a = 2; b = -14; c = -5;
Δ = b2-4ac
Δ = -142-4·2·(-5)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{59}}{2*2}=\frac{14-2\sqrt{59}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{59}}{2*2}=\frac{14+2\sqrt{59}}{4}
$