7x^2=14x+29

Solution for 7x^2=14x+29 equation:

7x^2=14x+29

We move all terms to the left:

7x^2-(14x+29)=0

We get rid of parentheses

7x^2-14x-29=0

a = 7; b = -14; c = -29;
Δ = b2-4ac
Δ = -142-4·7·(-29)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-12\sqrt{7}}{2*7}=\frac{14-12\sqrt{7}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+12\sqrt{7}}{2*7}=\frac{14+12\sqrt{7}}{14}
$