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610=12000/x+7x
We move all terms to the left:
610-(12000/x+7x)=0
Domain of the equation: x+7x)!=0We add all the numbers together, and all the variables
x∈R
-(+7x+12000/x)+610=0
We get rid of parentheses
-7x-12000/x+610=0
We multiply all the terms by the denominator
-7x*x+610*x-12000=0
We add all the numbers together, and all the variables
610x-7x*x-12000=0
Wy multiply elements
-7x^2+610x-12000=0
a = -7; b = 610; c = -12000;
Δ = b2-4ac
Δ = 6102-4·(-7)·(-12000)
Δ = 36100
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{36100}=190$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(610)-190}{2*-7}=\frac{-800}{-14} =57+1/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(610)+190}{2*-7}=\frac{-420}{-14} =+30 $
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