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-4/5x+2/3=13/4x+2
We move all terms to the left:
-4/5x+2/3-(13/4x+2)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 4x+2)!=0We get rid of parentheses
x∈R
-4/5x-13/4x-2+2/3=0
We calculate fractions
160x^2/180x^2+(-144x)/180x^2+(-585x)/180x^2-2=0
We multiply all the terms by the denominator
160x^2+(-144x)+(-585x)-2*180x^2=0
Wy multiply elements
160x^2-360x^2+(-144x)+(-585x)=0
We get rid of parentheses
160x^2-360x^2-144x-585x=0
We add all the numbers together, and all the variables
-200x^2-729x=0
a = -200; b = -729; c = 0;
Δ = b2-4ac
Δ = -7292-4·(-200)·0
Δ = 531441
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{531441}=729$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-729)-729}{2*-200}=\frac{0}{-400} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-729)+729}{2*-200}=\frac{1458}{-400} =-3+129/200 $
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