4x+2=1/2x+7

Solution for 4x+2=1/2x+7 equation:

4x+2=1/2x+7

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2-14x+4x-1=0

We add all the numbers together, and all the variables

8x^2-10x-1=0

a = 8; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·8·(-1)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{33}}{2*8}=\frac{10-2\sqrt{33}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{33}}{2*8}=\frac{10+2\sqrt{33}}{16}
$