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

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

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

We move all terms to the left:

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


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2-x^2+5x^2-5=0

We add all the numbers together, and all the variables

7x^2-5=0

a = 7; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·7·(-5)
Δ = 140
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{35}}{2*7}=\frac{0-2\sqrt{35}}{14}
=-\frac{2\sqrt{35}}{14}
=-\frac{\sqrt{35}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{35}}{2*7}=\frac{0+2\sqrt{35}}{14}
=\frac{2\sqrt{35}}{14}
=\frac{\sqrt{35}}{7}
$