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(3/5)x+1=25/9
We move all terms to the left:
(3/5)x+1-(25/9)=0
Domain of the equation: 5)x!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+3/5)x+1-(+25/9)=0
We multiply parentheses
3x^2+1-(+25/9)=0
We get rid of parentheses
3x^2+1-25/9=0
We multiply all the terms by the denominator
3x^2*9-25+1*9=0
We add all the numbers together, and all the variables
3x^2*9-16=0
Wy multiply elements
27x^2-16=0
a = 27; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·27·(-16)
Δ = 1728
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*27}=\frac{0-24\sqrt{3}}{54} =-\frac{24\sqrt{3}}{54} =-\frac{4\sqrt{3}}{9} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*27}=\frac{0+24\sqrt{3}}{54} =\frac{24\sqrt{3}}{54} =\frac{4\sqrt{3}}{9} $
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