5/6x+7=12-5/12x

Solution for 5/6x+7=12-5/12x equation:

5/6x+7=12-5/12x

We move all terms to the left:

5/6x+7-(12-5/12x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-(-5/12x+12)+7=0

We get rid of parentheses

5/6x+5/12x-12+7=0

We calculate fractions


60x/72x^2+30x/72x^2-12+7=0

We add all the numbers together, and all the variables

60x/72x^2+30x/72x^2-5=0

We multiply all the terms by the denominator


60x+30x-5*72x^2=0

We add all the numbers together, and all the variables

90x-5*72x^2=0

Wy multiply elements

-360x^2+90x=0

a = -360; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-360)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-360}=\frac{-180}{-720}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-360}=\frac{0}{-720}
=0
$