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

Solution for 7/2x+2/2=3x-4 equation:

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

7/2x-(3x-4)+1=0

We get rid of parentheses

7/2x-3x+4+1=0

We multiply all the terms by the denominator


-3x*2x+4*2x+1*2x+7=0

Wy multiply elements

-6x^2+8x+2x+7=0

We add all the numbers together, and all the variables

-6x^2+10x+7=0

a = -6; b = 10; c = +7;
Δ = b2-4ac
Δ = 102-4·(-6)·7
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{67}}{2*-6}=\frac{-10-2\sqrt{67}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{67}}{2*-6}=\frac{-10+2\sqrt{67}}{-12}
$