x=1/2(6x)+18

Solution for x=1/2(6x)+18 equation:

x=1/2(6x)+18

We move all terms to the left:

x-(1/2(6x)+18)=0


Domain of the equation: 26x+18)!=0

x∈R


We get rid of parentheses

x-1/26x-18=0

We multiply all the terms by the denominator


x*26x-18*26x-1=0

Wy multiply elements

26x^2-468x-1=0

a = 26; b = -468; c = -1;
Δ = b2-4ac
Δ = -4682-4·26·(-1)
Δ = 219128
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:

$\sqrt{\Delta}=\sqrt{219128}=\sqrt{196*1118}=\sqrt{196}*\sqrt{1118}=14\sqrt{1118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-468)-14\sqrt{1118}}{2*26}=\frac{468-14\sqrt{1118}}{52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-468)+14\sqrt{1118}}{2*26}=\frac{468+14\sqrt{1118}}{52}
$