/2x+6=4x+10

Solution for /2x+6=4x+10 equation:

/2x+6=4x+10

We move all terms to the left:

/2x+6-(4x+10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

/2x-4x-10+6=0

We multiply all the terms by the denominator


-4x*2x-10*2x+6*2x+=0

We add all the numbers together, and all the variables

-4x*2x-10*2x+6*2x=0

Wy multiply elements

-8x^2-20x+12x=0

We add all the numbers together, and all the variables

-8x^2-8x=0

a = -8; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-8)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-8}=\frac{16}{-16}
=-1
$