14x^2=2x+52

Solution for 14x^2=2x+52 equation:

14x^2=2x+52

We move all terms to the left:

14x^2-(2x+52)=0

We get rid of parentheses

14x^2-2x-52=0

a = 14; b = -2; c = -52;
Δ = b2-4ac
Δ = -22-4·14·(-52)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-54}{2*14}=\frac{-52}{28}
=-1+6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+54}{2*14}=\frac{56}{28}
=2
$