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-2/4x+3=1/5x+11
We move all terms to the left:
-2/4x+3-(1/5x+11)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 5x+11)!=0We get rid of parentheses
x∈R
-2/4x-1/5x-11+3=0
We calculate fractions
(-10x)/20x^2+(-4x)/20x^2-11+3=0
We add all the numbers together, and all the variables
(-10x)/20x^2+(-4x)/20x^2-8=0
We multiply all the terms by the denominator
(-10x)+(-4x)-8*20x^2=0
Wy multiply elements
-160x^2+(-10x)+(-4x)=0
We get rid of parentheses
-160x^2-10x-4x=0
We add all the numbers together, and all the variables
-160x^2-14x=0
a = -160; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-160)·0
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-160}=\frac{0}{-320} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-160}=\frac{28}{-320} =-7/80 $
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