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-1/2x-11=-x+12
We move all terms to the left:
-1/2x-11-(-x+12)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
-1/2x-(-1x+12)-11=0
We get rid of parentheses
-1/2x+1x-12-11=0
We multiply all the terms by the denominator
1x*2x-12*2x-11*2x-1=0
Wy multiply elements
2x^2-24x-22x-1=0
We add all the numbers together, and all the variables
2x^2-46x-1=0
a = 2; b = -46; c = -1;
Δ = b2-4ac
Δ = -462-4·2·(-1)
Δ = 2124
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2124}=\sqrt{36*59}=\sqrt{36}*\sqrt{59}=6\sqrt{59}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-6\sqrt{59}}{2*2}=\frac{46-6\sqrt{59}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+6\sqrt{59}}{2*2}=\frac{46+6\sqrt{59}}{4} $
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