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X-4/5X=18
We move all terms to the left:
X-4/5X-(18)=0
Domain of the equation: 5X!=0We multiply all the terms by the denominator
X!=0/5
X!=0
X∈R
X*5X-18*5X-4=0
Wy multiply elements
5X^2-90X-4=0
a = 5; b = -90; c = -4;
Δ = b2-4ac
Δ = -902-4·5·(-4)
Δ = 8180
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8180}=\sqrt{4*2045}=\sqrt{4}*\sqrt{2045}=2\sqrt{2045}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2045}}{2*5}=\frac{90-2\sqrt{2045}}{10} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2045}}{2*5}=\frac{90+2\sqrt{2045}}{10} $
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