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5x+7=2/3x=20
We move all terms to the left:
5x+7-(2/3x)=0
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5x-(+2/3x)+7=0
We get rid of parentheses
5x-2/3x+7=0
We multiply all the terms by the denominator
5x*3x+7*3x-2=0
Wy multiply elements
15x^2+21x-2=0
a = 15; b = 21; c = -2;
Δ = b2-4ac
Δ = 212-4·15·(-2)
Δ = 561
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{-(21)-\sqrt{561}}{2*15}=\frac{-21-\sqrt{561}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{561}}{2*15}=\frac{-21+\sqrt{561}}{30} $
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