(1+7x)6(7x)=36

Solution for (1+7x)6(7x)=36 equation:

(1+7x)6(7x)=36

We move all terms to the left:

(1+7x)6(7x)-(36)=0

We add all the numbers together, and all the variables

(7x+1)67x-36=0

We multiply parentheses

469x^2+67x-36=0

a = 469; b = 67; c = -36;
Δ = b2-4ac
Δ = 672-4·469·(-36)
Δ = 72025
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:

$\sqrt{\Delta}=\sqrt{72025}=\sqrt{25*2881}=\sqrt{25}*\sqrt{2881}=5\sqrt{2881}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(67)-5\sqrt{2881}}{2*469}=\frac{-67-5\sqrt{2881}}{938}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+5\sqrt{2881}}{2*469}=\frac{-67+5\sqrt{2881}}{938}
$