3/4x=-6x+18

Solution for 3/4x=-6x+18 equation:

3/4x=-6x+18

We move all terms to the left:

3/4x-(-6x+18)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x+6x-18=0

We multiply all the terms by the denominator


6x*4x-18*4x+3=0

Wy multiply elements

24x^2-72x+3=0

a = 24; b = -72; c = +3;
Δ = b2-4ac
Δ = -722-4·24·3
Δ = 4896
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:

$\sqrt{\Delta}=\sqrt{4896}=\sqrt{144*34}=\sqrt{144}*\sqrt{34}=12\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{34}}{2*24}=\frac{72-12\sqrt{34}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{34}}{2*24}=\frac{72+12\sqrt{34}}{48}
$