1/2x-4=-x+7

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

1/2x-4=-x+7

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


1x*2x-7*2x-4*2x+1=0

Wy multiply elements

2x^2-14x-8x+1=0

We add all the numbers together, and all the variables

2x^2-22x+1=0

a = 2; b = -22; c = +1;
Δ = b2-4ac
Δ = -222-4·2·1
Δ = 476
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:

$\sqrt{\Delta}=\sqrt{476}=\sqrt{4*119}=\sqrt{4}*\sqrt{119}=2\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{119}}{2*2}=\frac{22-2\sqrt{119}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{119}}{2*2}=\frac{22+2\sqrt{119}}{4}
$