(3/4)x=9-18x

Solution for (3/4)x=9-18x equation:

(3/4)x=9-18x

We move all terms to the left:

(3/4)x-(9-18x)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/4)x-(-18x+9)=0

We multiply parentheses

3x^2-(-18x+9)=0

We get rid of parentheses

3x^2+18x-9=0

a = 3; b = 18; c = -9;
Δ = b2-4ac
Δ = 182-4·3·(-9)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12\sqrt{3}}{2*3}=\frac{-18-12\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12\sqrt{3}}{2*3}=\frac{-18+12\sqrt{3}}{6}
$