7/2x+2=5x+4

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

7/2x+2=5x+4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-10x^2-8x+4x+7=0

We add all the numbers together, and all the variables

-10x^2-4x+7=0

a = -10; b = -4; c = +7;
Δ = b2-4ac
Δ = -42-4·(-10)·7
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{74}}{2*-10}=\frac{4-2\sqrt{74}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{74}}{2*-10}=\frac{4+2\sqrt{74}}{-20}
$