7(x+6)7x=9

Solution for 7(x+6)7x=9 equation:

7(x+6)7x=9

We move all terms to the left:

7(x+6)7x-(9)=0

We multiply parentheses

49x^2+294x-9=0

a = 49; b = 294; c = -9;
Δ = b2-4ac
Δ = 2942-4·49·(-9)
Δ = 88200
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:

$\sqrt{\Delta}=\sqrt{88200}=\sqrt{44100*2}=\sqrt{44100}*\sqrt{2}=210\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(294)-210\sqrt{2}}{2*49}=\frac{-294-210\sqrt{2}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(294)+210\sqrt{2}}{2*49}=\frac{-294+210\sqrt{2}}{98}
$