(7x)^2=2x+6

Solution for (7x)^2=2x+6 equation:

(7x)^2=2x+6

We move all terms to the left:

(7x)^2-(2x+6)=0

We get rid of parentheses

7x^2-2x-6=0

a = 7; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·7·(-6)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{43}}{2*7}=\frac{2-2\sqrt{43}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{43}}{2*7}=\frac{2+2\sqrt{43}}{14}
$