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3/4x+1/2x=5
We move all terms to the left:
3/4x+1/2x-(5)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x!=0We calculate fractions
x!=0/2
x!=0
x∈R
6x/8x^2+4x/8x^2-5=0
We multiply all the terms by the denominator
6x+4x-5*8x^2=0
We add all the numbers together, and all the variables
10x-5*8x^2=0
Wy multiply elements
-40x^2+10x=0
a = -40; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-40)·0
Δ = 100
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{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-40}=\frac{-20}{-80} =1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-40}=\frac{0}{-80} =0 $
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