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(5/2)x=17/4
We move all terms to the left:
(5/2)x-(17/4)=0
Domain of the equation: 2)x!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+5/2)x-(+17/4)=0
We multiply parentheses
5x^2-(+17/4)=0
We get rid of parentheses
5x^2-17/4=0
We multiply all the terms by the denominator
5x^2*4-17=0
Wy multiply elements
20x^2-17=0
a = 20; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·20·(-17)
Δ = 1360
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{85}}{2*20}=\frac{0-4\sqrt{85}}{40} =-\frac{4\sqrt{85}}{40} =-\frac{\sqrt{85}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{85}}{2*20}=\frac{0+4\sqrt{85}}{40} =\frac{4\sqrt{85}}{40} =\frac{\sqrt{85}}{10} $
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