X=6/7x+12

Solution for X=6/7x+12 equation:

X=6/7X+12

We move all terms to the left:

X-(6/7X+12)=0


Domain of the equation: 7X+12)!=0

X∈R


We get rid of parentheses

X-6/7X-12=0

We multiply all the terms by the denominator


X*7X-12*7X-6=0

Wy multiply elements

7X^2-84X-6=0

a = 7; b = -84; c = -6;
Δ = b2-4ac
Δ = -842-4·7·(-6)
Δ = 7224
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:

$\sqrt{\Delta}=\sqrt{7224}=\sqrt{4*1806}=\sqrt{4}*\sqrt{1806}=2\sqrt{1806}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1806}}{2*7}=\frac{84-2\sqrt{1806}}{14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1806}}{2*7}=\frac{84+2\sqrt{1806}}{14}
$