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-12/5x+-2/3x=-31/75
We move all terms to the left:
-12/5x+-2/3x-(-31/75)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-12/5x-2/3x-(-31/75)=0
We get rid of parentheses
-12/5x-2/3x+31/75=0
We calculate fractions
1395x^2/7875x^2+(-18900x)/7875x^2+(-5250x)/7875x^2=0
We multiply all the terms by the denominator
1395x^2+(-18900x)+(-5250x)=0
We get rid of parentheses
1395x^2-18900x-5250x=0
We add all the numbers together, and all the variables
1395x^2-24150x=0
a = 1395; b = -24150; c = 0;
Δ = b2-4ac
Δ = -241502-4·1395·0
Δ = 583222500
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{583222500}=24150$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24150)-24150}{2*1395}=\frac{0}{2790} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24150)+24150}{2*1395}=\frac{48300}{2790} =17+29/93 $
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