7x^2-49=7x

Solution for 7x^2-49=7x equation:

7x^2-49=7x

We move all terms to the left:

7x^2-49-(7x)=0

a = 7; b = -7; c = -49;
Δ = b2-4ac
Δ = -72-4·7·(-49)
Δ = 1421
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:

$\sqrt{\Delta}=\sqrt{1421}=\sqrt{49*29}=\sqrt{49}*\sqrt{29}=7\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7\sqrt{29}}{2*7}=\frac{7-7\sqrt{29}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7\sqrt{29}}{2*7}=\frac{7+7\sqrt{29}}{14}
$