7+5x=1/2x+2

Solution for 7+5x=1/2x+2 equation:

7+5x=1/2x+2

We move all terms to the left:

7+5x-(1/2x+2)=0


Domain of the equation: 2x+2)!=0

x∈R


We get rid of parentheses

5x-1/2x-2+7=0

We multiply all the terms by the denominator


5x*2x-2*2x+7*2x-1=0

Wy multiply elements

10x^2-4x+14x-1=0

We add all the numbers together, and all the variables

10x^2+10x-1=0

a = 10; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·10·(-1)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{35}}{2*10}=\frac{-10-2\sqrt{35}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{35}}{2*10}=\frac{-10+2\sqrt{35}}{20}
$