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3/7+5(3x-2)=15/9-(3x-5x)+20
We move all terms to the left:
3/7+5(3x-2)-(15/9-(3x-5x)+20)=0
Domain of the equation: 9-(3x-5x)+20)!=0We add all the numbers together, and all the variables
We move all terms containing x to the left, all other terms to the right
-(3x-5x)+20)!=-9
x∈R
5(3x-2)-(15/9-(-2x)+20)+3/7=0
We multiply parentheses
15x-(15/9-(-2x)+20)-10+3/7=0
We calculate fractions
15x+()/2x+2x/2x-10=0
Fractions to decimals
()/2x+15x-10+1=0
We multiply all the terms by the denominator
15x*2x-10*2x+1*2x+()=0
We add all the numbers together, and all the variables
15x*2x-10*2x+1*2x=0
Wy multiply elements
30x^2-20x+2x=0
We add all the numbers together, and all the variables
30x^2-18x=0
a = 30; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·30·0
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*30}=\frac{0}{60} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*30}=\frac{36}{60} =3/5 $
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