Answer:
X = 11/20
Step-by-step explanation:
7/4x-3=2+9/2x
We move all terms to the left:
7/4x-3-(2+9/2x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
7/4x-(9/2x+2)-3=0
We get rid of parentheses
7/4x-9/2x-2-3=0
We calculate fractions
14x/8x^2+(-36x)/8x^2-2-3=0
We add all the numbers together, and all the variables
14x/8x^2+(-36x)/8x^2-5=0
We multiply all the terms by the denominator
14x+(-36x)-5*8x^2=0
Wy multiply elements
-40x^2+14x+(-36x)=0
We get rid of parentheses
-40x^2+14x-36x=0
We add all the numbers together, and all the variables
-40x^2-22x=0
a = -40; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-40)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
x1=−b−Δ√2ax2=−b+Δ√2a
Δ−−√=484−−−√=22
x1=−b−Δ√2a=−(−22)−222∗−40=0−80=0
x2=−b+Δ√2a=−(−22)+222∗−40=44−80=−11/20
