(9/4)x=2x+9

Solution for (9/4)x=2x+9 equation:

(9/4)x=2x+9

We move all terms to the left:

(9/4)x-(2x+9)=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

(+9/4)x-(2x+9)=0

We multiply parentheses

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

We get rid of parentheses

9x^2-2x-9=0

a = 9; b = -2; c = -9;
Δ = b2-4ac
Δ = -22-4·9·(-9)
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{82}}{2*9}=\frac{2-2\sqrt{82}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{82}}{2*9}=\frac{2+2\sqrt{82}}{18}
$