X=6/7u+7

Solution for X=6/7u+7 equation:

X=6/7X+7

We move all terms to the left:

X-(6/7X+7)=0


Domain of the equation: 7X+7)!=0

X∈R


We get rid of parentheses

X-6/7X-7=0

We multiply all the terms by the denominator


X*7X-7*7X-6=0

Wy multiply elements

7X^2-49X-6=0

a = 7; b = -49; c = -6;
Δ = b2-4ac
Δ = -492-4·7·(-6)
Δ = 2569
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{-(-49)-\sqrt{2569}}{2*7}=\frac{49-\sqrt{2569}}{14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{2569}}{2*7}=\frac{49+\sqrt{2569}}{14}
$