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2/5x-2=1x-12
We move all terms to the left:
2/5x-2-(1x-12)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
2/5x-(x-12)-2=0
We get rid of parentheses
2/5x-x+12-2=0
We multiply all the terms by the denominator
-x*5x+12*5x-2*5x+2=0
Wy multiply elements
-5x^2+60x-10x+2=0
We add all the numbers together, and all the variables
-5x^2+50x+2=0
a = -5; b = 50; c = +2;
Δ = b2-4ac
Δ = 502-4·(-5)·2
Δ = 2540
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2540}=\sqrt{4*635}=\sqrt{4}*\sqrt{635}=2\sqrt{635}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{635}}{2*-5}=\frac{-50-2\sqrt{635}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{635}}{2*-5}=\frac{-50+2\sqrt{635}}{-10} $
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