/4x+6=2x-8

Solution for /4x+6=2x-8 equation:

/4x+6=2x-8

We move all terms to the left:

/4x+6-(2x-8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

/4x-2x+8+6=0

We multiply all the terms by the denominator


-2x*4x+8*4x+6*4x+=0

We add all the numbers together, and all the variables

-2x*4x+8*4x+6*4x=0

Wy multiply elements

-8x^2+32x+24x=0

We add all the numbers together, and all the variables

-8x^2+56x=0

a = -8; b = 56; c = 0;
Δ = b2-4ac
Δ = 562-4·(-8)·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-56}{2*-8}=\frac{-112}{-16}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+56}{2*-8}=\frac{0}{-16}
=0
$