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

Solution for -(1)/(2)x+7=2x+3 equation:

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-6x+14x-1=0

We add all the numbers together, and all the variables

-4x^2+8x-1=0

a = -4; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·(-4)·(-1)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{3}}{2*-4}=\frac{-8-4\sqrt{3}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{3}}{2*-4}=\frac{-8+4\sqrt{3}}{-8}
$