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2/2x=7/5x+4
We move all terms to the left:
2/2x-(7/5x+4)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 5x+4)!=0We get rid of parentheses
x∈R
2/2x-7/5x-4=0
We calculate fractions
10x/10x^2+(-14x)/10x^2-4=0
We multiply all the terms by the denominator
10x+(-14x)-4*10x^2=0
Wy multiply elements
-40x^2+10x+(-14x)=0
We get rid of parentheses
-40x^2+10x-14x=0
We add all the numbers together, and all the variables
-40x^2-4x=0
a = -40; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-40)·0
Δ = 16
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{16}=4$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-40}=\frac{0}{-80} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-40}=\frac{8}{-80} =-1/10 $
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