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6/8x+7=x
We move all terms to the left:
6/8x+7-(x)=0
Domain of the equation: 8x!=0We add all the numbers together, and all the variables
x!=0/8
x!=0
x∈R
-1x+6/8x+7=0
We multiply all the terms by the denominator
-1x*8x+7*8x+6=0
Wy multiply elements
-8x^2+56x+6=0
a = -8; b = 56; c = +6;
Δ = b2-4ac
Δ = 562-4·(-8)·6
Δ = 3328
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3328}=\sqrt{256*13}=\sqrt{256}*\sqrt{13}=16\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-16\sqrt{13}}{2*-8}=\frac{-56-16\sqrt{13}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+16\sqrt{13}}{2*-8}=\frac{-56+16\sqrt{13}}{-16} $
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