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3/5x+8=x
We move all terms to the left:
3/5x+8-(x)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
-1x+3/5x+8=0
We multiply all the terms by the denominator
-1x*5x+8*5x+3=0
Wy multiply elements
-5x^2+40x+3=0
a = -5; b = 40; c = +3;
Δ = b2-4ac
Δ = 402-4·(-5)·3
Δ = 1660
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1660}=\sqrt{4*415}=\sqrt{4}*\sqrt{415}=2\sqrt{415}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{415}}{2*-5}=\frac{-40-2\sqrt{415}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{415}}{2*-5}=\frac{-40+2\sqrt{415}}{-10} $
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