x=4/7x+18

Solution for x=4/7x+18 equation:

x=4/7x+18

We move all terms to the left:

x-(4/7x+18)=0


Domain of the equation: 7x+18)!=0

x∈R


We get rid of parentheses

x-4/7x-18=0

We multiply all the terms by the denominator


x*7x-18*7x-4=0

Wy multiply elements

7x^2-126x-4=0

a = 7; b = -126; c = -4;
Δ = b2-4ac
Δ = -1262-4·7·(-4)
Δ = 15988
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:

$\sqrt{\Delta}=\sqrt{15988}=\sqrt{4*3997}=\sqrt{4}*\sqrt{3997}=2\sqrt{3997}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3997}}{2*7}=\frac{126-2\sqrt{3997}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3997}}{2*7}=\frac{126+2\sqrt{3997}}{14}
$