x=-1/2x+14

Solution for x=-1/2x+14 equation:

x=-1/2x+14

We move all terms to the left:

x-(-1/2x+14)=0


Domain of the equation: 2x+14)!=0

x∈R


We get rid of parentheses

x+1/2x-14=0

We multiply all the terms by the denominator


x*2x-14*2x+1=0

Wy multiply elements

2x^2-28x+1=0

a = 2; b = -28; c = +1;
Δ = b2-4ac
Δ = -282-4·2·1
Δ = 776
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:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{194}}{2*2}=\frac{28-2\sqrt{194}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{194}}{2*2}=\frac{28+2\sqrt{194}}{4}
$