7/4x+6/8x=36/12

Solution for 7/4x+6/8x=36/12 equation:

7/4x+6/8x=36/12

We move all terms to the left:

7/4x+6/8x-(36/12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

7/4x+6/8x-3=0

We calculate fractions


56x/32x^2+24x/32x^2-3=0

We multiply all the terms by the denominator


56x+24x-3*32x^2=0

We add all the numbers together, and all the variables

80x-3*32x^2=0

Wy multiply elements

-96x^2+80x=0

a = -96; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·(-96)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-80}{2*-96}=\frac{-160}{-192}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*-96}=\frac{0}{-192}
=0
$