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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-180x^2)/48x^2+12x/48x^2+32x/48x^2-4+4=0

We add all the numbers together, and all the variables

(-180x^2)/48x^2+12x/48x^2+32x/48x^2=0

We multiply all the terms by the denominator


(-180x^2)+12x+32x=0

We add all the numbers together, and all the variables

(-180x^2)+44x=0

We get rid of parentheses

-180x^2+44x=0

a = -180; b = 44; c = 0;
Δ = b2-4ac
Δ = 442-4·(-180)·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-44}{2*-180}=\frac{-88}{-360}
=11/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+44}{2*-180}=\frac{0}{-360}
=0
$