3/4x-18x=24

Solution for 3/4x-18x=24 equation:

3/4x-18x=24

We move all terms to the left:

3/4x-18x-(24)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-18x+3/4x-24=0

We multiply all the terms by the denominator


-18x*4x-24*4x+3=0

Wy multiply elements

-72x^2-96x+3=0

a = -72; b = -96; c = +3;
Δ = b2-4ac
Δ = -962-4·(-72)·3
Δ = 10080
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:

$\sqrt{\Delta}=\sqrt{10080}=\sqrt{144*70}=\sqrt{144}*\sqrt{70}=12\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-12\sqrt{70}}{2*-72}=\frac{96-12\sqrt{70}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+12\sqrt{70}}{2*-72}=\frac{96+12\sqrt{70}}{-144}
$