-4/8x+4=3/4x-11

Solution for -4/8x+4=3/4x-11 equation:

-4/8x+4=3/4x-11

We move all terms to the left:

-4/8x+4-(3/4x-11)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x-11)!=0

x∈R


We get rid of parentheses

-4/8x-3/4x+11+4=0

We calculate fractions


(-16x)/32x^2+(-24x)/32x^2+11+4=0

We add all the numbers together, and all the variables

(-16x)/32x^2+(-24x)/32x^2+15=0

We multiply all the terms by the denominator


(-16x)+(-24x)+15*32x^2=0

Wy multiply elements

480x^2+(-16x)+(-24x)=0

We get rid of parentheses

480x^2-16x-24x=0

We add all the numbers together, and all the variables

480x^2-40x=0

a = 480; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·480·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*480}=\frac{0}{960}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*480}=\frac{80}{960}
=1/12
$