6x+(x-9)7x=116

Solution for 6x+(x-9)7x=116 equation:

6x+(x-9)7x=116

We move all terms to the left:

6x+(x-9)7x-(116)=0

We multiply parentheses

7x^2+6x-63x-116=0

We add all the numbers together, and all the variables

7x^2-57x-116=0

a = 7; b = -57; c = -116;
Δ = b2-4ac
Δ = -572-4·7·(-116)
Δ = 6497
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-\sqrt{6497}}{2*7}=\frac{57-\sqrt{6497}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+\sqrt{6497}}{2*7}=\frac{57+\sqrt{6497}}{14}
$