1/2(7x)=x+4

Solution for 1/2(7x)=x+4 equation:

1/2(7x)=x+4

We move all terms to the left:

1/2(7x)-(x+4)=0


Domain of the equation: 27x!=0

x!=0/27

x!=0

x∈R


We get rid of parentheses

1/27x-x-4=0

We multiply all the terms by the denominator


-x*27x-4*27x+1=0

Wy multiply elements

-27x^2-108x+1=0

a = -27; b = -108; c = +1;
Δ = b2-4ac
Δ = -1082-4·(-27)·1
Δ = 11772
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:

$\sqrt{\Delta}=\sqrt{11772}=\sqrt{36*327}=\sqrt{36}*\sqrt{327}=6\sqrt{327}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-6\sqrt{327}}{2*-27}=\frac{108-6\sqrt{327}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+6\sqrt{327}}{2*-27}=\frac{108+6\sqrt{327}}{-54}
$