-1/4x+10=2/3x-6

Solution for -1/4x+10=2/3x-6 equation:

-1/4x+10=2/3x-6

We move all terms to the left:

-1/4x+10-(2/3x-6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-6)!=0

x∈R


We get rid of parentheses

-1/4x-2/3x+6+10=0

We calculate fractions


(-3x)/12x^2+(-8x)/12x^2+6+10=0

We add all the numbers together, and all the variables

(-3x)/12x^2+(-8x)/12x^2+16=0

We multiply all the terms by the denominator


(-3x)+(-8x)+16*12x^2=0

Wy multiply elements

192x^2+(-3x)+(-8x)=0

We get rid of parentheses

192x^2-3x-8x=0

We add all the numbers together, and all the variables

192x^2-11x=0

a = 192; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·192·0
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*192}=\frac{0}{384}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*192}=\frac{22}{384}
=11/192
$