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-6/5x+2/5=-7/2x-3
We move all terms to the left:
-6/5x+2/5-(-7/2x-3)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 2x-3)!=0We get rid of parentheses
x∈R
-6/5x+7/2x+3+2/5=0
We calculate fractions
(-12x)/250x^2+875x/250x^2+4x/250x^2+3=0
We multiply all the terms by the denominator
(-12x)+875x+4x+3*250x^2=0
We add all the numbers together, and all the variables
879x+(-12x)+3*250x^2=0
Wy multiply elements
750x^2+879x+(-12x)=0
We get rid of parentheses
750x^2+879x-12x=0
We add all the numbers together, and all the variables
750x^2+867x=0
a = 750; b = 867; c = 0;
Δ = b2-4ac
Δ = 8672-4·750·0
Δ = 751689
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{751689}=867$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(867)-867}{2*750}=\frac{-1734}{1500} =-1+39/250 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(867)+867}{2*750}=\frac{0}{1500} =0 $
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