x-7/2x+4=2

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

x-7/2x+4=2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x-7/2x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2+4x-7=0

a = 2; b = 4; c = -7;
Δ = b2-4ac
Δ = 42-4·2·(-7)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{2}}{2*2}=\frac{-4-6\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{2}}{2*2}=\frac{-4+6\sqrt{2}}{4}
$