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x=-1/8x+3.75
We move all terms to the left:
x-(-1/8x+3.75)=0
Domain of the equation: 8x+3.75)!=0We get rid of parentheses
x∈R
x+1/8x-3.75=0
We multiply all the terms by the denominator
x*8x-(3.75)*8x+1=0
We multiply parentheses
x*8x-30x+1=0
Wy multiply elements
8x^2-30x+1=0
a = 8; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·8·1
Δ = 868
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{217}}{2*8}=\frac{30-2\sqrt{217}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{217}}{2*8}=\frac{30+2\sqrt{217}}{16} $
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