4x^2=2x+14

Solution for 4x^2=2x+14 equation:

4x^2=2x+14

We move all terms to the left:

4x^2-(2x+14)=0

We get rid of parentheses

4x^2-2x-14=0

a = 4; b = -2; c = -14;
Δ = b2-4ac
Δ = -22-4·4·(-14)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{57}}{2*4}=\frac{2-2\sqrt{57}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{57}}{2*4}=\frac{2+2\sqrt{57}}{8}
$