3/4x+7x=72

Solution for 3/4x+7x=72 equation:

3/4x+7x=72

We move all terms to the left:

3/4x+7x-(72)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

7x+3/4x-72=0

We multiply all the terms by the denominator


7x*4x-72*4x+3=0

Wy multiply elements

28x^2-288x+3=0

a = 28; b = -288; c = +3;
Δ = b2-4ac
Δ = -2882-4·28·3
Δ = 82608
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:

$\sqrt{\Delta}=\sqrt{82608}=\sqrt{16*5163}=\sqrt{16}*\sqrt{5163}=4\sqrt{5163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-4\sqrt{5163}}{2*28}=\frac{288-4\sqrt{5163}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+4\sqrt{5163}}{2*28}=\frac{288+4\sqrt{5163}}{56}
$