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7/8x+5=x
We move all terms to the left:
7/8x+5-(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+7/8x+5=0
We multiply all the terms by the denominator
-1x*8x+5*8x+7=0
Wy multiply elements
-8x^2+40x+7=0
a = -8; b = 40; c = +7;
Δ = b2-4ac
Δ = 402-4·(-8)·7
Δ = 1824
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{114}}{2*-8}=\frac{-40-4\sqrt{114}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{114}}{2*-8}=\frac{-40+4\sqrt{114}}{-16} $
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