1/2x-5+2/3x=7/6+4

Solution for 1/2x-5+2/3x=7/6+4 equation:

1/2x-5+2/3x=7/6+4

We move all terms to the left:

1/2x-5+2/3x-(7/6+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/2x+2/3x-5-4-7/6=0

We calculate fractions


(-126x^2)/216x^2+108x/216x^2+144x/216x^2-5-4=0

We add all the numbers together, and all the variables

(-126x^2)/216x^2+108x/216x^2+144x/216x^2-9=0

We multiply all the terms by the denominator


(-126x^2)+108x+144x-9*216x^2=0

We add all the numbers together, and all the variables

(-126x^2)+252x-9*216x^2=0

Wy multiply elements

(-126x^2)-1944x^2+252x=0

We get rid of parentheses

-126x^2-1944x^2+252x=0

We add all the numbers together, and all the variables

-2070x^2+252x=0

a = -2070; b = 252; c = 0;
Δ = b2-4ac
Δ = 2522-4·(-2070)·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-252}{2*-2070}=\frac{-504}{-4140}
=14/115
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+252}{2*-2070}=\frac{0}{-4140}
=0
$