4+5/2x-7=x-4/2x-7

Solution for 4+5/2x-7=x-4/2x-7 equation:

4+5/2x-7=x-4/2x-7

We move all terms to the left:

4+5/2x-7-(x-4/2x-7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x-7)!=0

x∈R


We add all the numbers together, and all the variables

5/2x-(x-4/2x-7)-3=0

We get rid of parentheses

5/2x-x+4/2x+7-3=0

We multiply all the terms by the denominator


-x*2x+7*2x-3*2x+5+4=0

We add all the numbers together, and all the variables

-x*2x+7*2x-3*2x+9=0

Wy multiply elements

-2x^2+14x-6x+9=0

We add all the numbers together, and all the variables

-2x^2+8x+9=0

a = -2; b = 8; c = +9;
Δ = b2-4ac
Δ = 82-4·(-2)·9
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{34}}{2*-2}=\frac{-8-2\sqrt{34}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{34}}{2*-2}=\frac{-8+2\sqrt{34}}{-4}
$