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2/5x+6-x=9
We move all terms to the left:
2/5x+6-x-(9)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
-1x+2/5x-3=0
We multiply all the terms by the denominator
-1x*5x-3*5x+2=0
Wy multiply elements
-5x^2-15x+2=0
a = -5; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·(-5)·2
Δ = 265
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{-(-15)-\sqrt{265}}{2*-5}=\frac{15-\sqrt{265}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{265}}{2*-5}=\frac{15+\sqrt{265}}{-10} $
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