/2x+5=x+7

Solution for /2x+5=x+7 equation:

/2x+5=x+7

We move all terms to the left:

/2x+5-(x+7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

/2x-x-7+5=0

We multiply all the terms by the denominator


-x*2x-7*2x+5*2x+=0

We add all the numbers together, and all the variables

-x*2x-7*2x+5*2x=0

Wy multiply elements

-2x^2-14x+10x=0

We add all the numbers together, and all the variables

-2x^2-4x=0

a = -2; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-2)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-2}=\frac{8}{-4}
=-2
$