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X+3/8X=121
We move all terms to the left:
X+3/8X-(121)=0
Domain of the equation: 8X!=0We multiply all the terms by the denominator
X!=0/8
X!=0
X∈R
X*8X-121*8X+3=0
Wy multiply elements
8X^2-968X+3=0
a = 8; b = -968; c = +3;
Δ = b2-4ac
Δ = -9682-4·8·3
Δ = 936928
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{936928}=\sqrt{16*58558}=\sqrt{16}*\sqrt{58558}=4\sqrt{58558}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-968)-4\sqrt{58558}}{2*8}=\frac{968-4\sqrt{58558}}{16} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-968)+4\sqrt{58558}}{2*8}=\frac{968+4\sqrt{58558}}{16} $
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