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x=-2/5x+4
We move all terms to the left:
x-(-2/5x+4)=0
Domain of the equation: 5x+4)!=0We get rid of parentheses
x∈R
x+2/5x-4=0
We multiply all the terms by the denominator
x*5x-4*5x+2=0
Wy multiply elements
5x^2-20x+2=0
a = 5; b = -20; c = +2;
Δ = b2-4ac
Δ = -202-4·5·2
Δ = 360
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{10}}{2*5}=\frac{20-6\sqrt{10}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{10}}{2*5}=\frac{20+6\sqrt{10}}{10} $
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