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0.25x=7-1/3x
We move all terms to the left:
0.25x-(7-1/3x)=0
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
0.25x-(-1/3x+7)=0
We get rid of parentheses
0.25x+1/3x-7=0
We multiply all the terms by the denominator
(0.25x)*3x-7*3x+1=0
We add all the numbers together, and all the variables
(+0.25x)*3x-7*3x+1=0
We multiply parentheses
0x^2-7*3x+1=0
Wy multiply elements
0x^2-21x+1=0
We add all the numbers together, and all the variables
x^2-21x+1=0
a = 1; b = -21; c = +1;
Δ = b2-4ac
Δ = -212-4·1·1
Δ = 437
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{437}}{2*1}=\frac{21-\sqrt{437}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{437}}{2*1}=\frac{21+\sqrt{437}}{2} $
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