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1/26x+4=2x+12
We move all terms to the left:
1/26x+4-(2x+12)=0
Domain of the equation: 26x!=0We get rid of parentheses
x!=0/26
x!=0
x∈R
1/26x-2x-12+4=0
We multiply all the terms by the denominator
-2x*26x-12*26x+4*26x+1=0
Wy multiply elements
-52x^2-312x+104x+1=0
We add all the numbers together, and all the variables
-52x^2-208x+1=0
a = -52; b = -208; c = +1;
Δ = b2-4ac
Δ = -2082-4·(-52)·1
Δ = 43472
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{43472}=\sqrt{16*2717}=\sqrt{16}*\sqrt{2717}=4\sqrt{2717}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-208)-4\sqrt{2717}}{2*-52}=\frac{208-4\sqrt{2717}}{-104} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-208)+4\sqrt{2717}}{2*-52}=\frac{208+4\sqrt{2717}}{-104} $
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