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(5/8)x=42
We move all terms to the left:
(5/8)x-(42)=0
Domain of the equation: 8)x!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+5/8)x-42=0
We multiply parentheses
5x^2-42=0
a = 5; b = 0; c = -42;
Δ = b2-4ac
Δ = 02-4·5·(-42)
Δ = 840
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*5}=\frac{0-2\sqrt{210}}{10} =-\frac{2\sqrt{210}}{10} =-\frac{\sqrt{210}}{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*5}=\frac{0+2\sqrt{210}}{10} =\frac{2\sqrt{210}}{10} =\frac{\sqrt{210}}{5} $
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