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3/4x+5=5/8x-2
We move all terms to the left:
3/4x+5-(5/8x-2)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 8x-2)!=0We get rid of parentheses
x∈R
3/4x-5/8x+2+5=0
We calculate fractions
24x/32x^2+(-20x)/32x^2+2+5=0
We add all the numbers together, and all the variables
24x/32x^2+(-20x)/32x^2+7=0
We multiply all the terms by the denominator
24x+(-20x)+7*32x^2=0
Wy multiply elements
224x^2+24x+(-20x)=0
We get rid of parentheses
224x^2+24x-20x=0
We add all the numbers together, and all the variables
224x^2+4x=0
a = 224; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·224·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*224}=\frac{-8}{448} =-1/56 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*224}=\frac{0}{448} =0 $
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