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9/4x(4-3)=9x+11
We move all terms to the left:
9/4x(4-3)-(9x+11)=0
Domain of the equation: 4x(4-3)!=0We add all the numbers together, and all the variables
x∈R
9/4x1-(9x+11)=0
We get rid of parentheses
9/4x1-9x-11=0
We multiply all the terms by the denominator
-9x*4x1-11*4x1+9=0
Wy multiply elements
-36x^2-44x+9=0
a = -36; b = -44; c = +9;
Δ = b2-4ac
Δ = -442-4·(-36)·9
Δ = 3232
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3232}=\sqrt{16*202}=\sqrt{16}*\sqrt{202}=4\sqrt{202}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{202}}{2*-36}=\frac{44-4\sqrt{202}}{-72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{202}}{2*-36}=\frac{44+4\sqrt{202}}{-72} $
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