-1/x-3=7/4x-12+2

Solution for -1/x-3=7/4x-12+2 equation:

-1/x-3=7/4x-12+2

We move all terms to the left:

-1/x-3-(7/4x-12+2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x-12+2)!=0

We move all terms containing x to the left, all other terms to the right

4x+2)!=12

x∈R


We add all the numbers together, and all the variables

-1/x-(7/4x-10)-3=0

We get rid of parentheses

-1/x-7/4x+10-3=0

We calculate fractions


(-4x)/4x^2+(-7x)/4x^2+10-3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


(-4x)+(-7x)+7*4x^2=0

Wy multiply elements

28x^2+(-4x)+(-7x)=0

We get rid of parentheses

28x^2-4x-7x=0

We add all the numbers together, and all the variables

28x^2-11x=0

a = 28; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·28·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*28}=\frac{0}{56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*28}=\frac{22}{56}
=11/28
$