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x-30/x=7
We move all terms to the left:
x-30/x-(7)=0
Domain of the equation: x!=0We multiply all the terms by the denominator
x∈R
x*x-7*x-30=0
We add all the numbers together, and all the variables
-7x+x*x-30=0
Wy multiply elements
x^2-7x-30=0
a = 1; b = -7; c = -30;
Δ = b2-4ac
Δ = -72-4·1·(-30)
Δ = 169
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{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*1}=\frac{-6}{2} =-3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*1}=\frac{20}{2} =10 $
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