2x^2=14x+7

Solution for 2x^2=14x+7 equation:

2x^2=14x+7

We move all terms to the left:

2x^2-(14x+7)=0

We get rid of parentheses

2x^2-14x-7=0

a = 2; b = -14; c = -7;
Δ = b2-4ac
Δ = -142-4·2·(-7)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{7}}{2*2}=\frac{14-6\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{7}}{2*2}=\frac{14+6\sqrt{7}}{4}
$