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5x+7=2/3x+20
We move all terms to the left:
5x+7-(2/3x+20)=0
Domain of the equation: 3x+20)!=0We get rid of parentheses
x∈R
5x-2/3x-20+7=0
We multiply all the terms by the denominator
5x*3x-20*3x+7*3x-2=0
Wy multiply elements
15x^2-60x+21x-2=0
We add all the numbers together, and all the variables
15x^2-39x-2=0
a = 15; b = -39; c = -2;
Δ = b2-4ac
Δ = -392-4·15·(-2)
Δ = 1641
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{1641}}{2*15}=\frac{39-\sqrt{1641}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1641}}{2*15}=\frac{39+\sqrt{1641}}{30} $
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