2x+3.5=-1/2x+7

Solution for 2x+3.5=-1/2x+7 equation:

2x+3.5=-1/2x+7

We move all terms to the left:

2x+3.5-(-1/2x+7)=0


Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

2x+1/2x-7+3.5=0

We multiply all the terms by the denominator


2x*2x-7*2x+(3.5)*2x+1=0

We multiply parentheses

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

Wy multiply elements

4x^2-14x+7x+1=0

We add all the numbers together, and all the variables

4x^2-7x+1=0

a = 4; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·4·1
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{33}}{2*4}=\frac{7-\sqrt{33}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{33}}{2*4}=\frac{7+\sqrt{33}}{8}
$