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48-3/5x=x
We move all terms to the left:
48-3/5x-(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+48=0
We multiply all the terms by the denominator
-1x*5x+48*5x-3=0
Wy multiply elements
-5x^2+240x-3=0
a = -5; b = 240; c = -3;
Δ = b2-4ac
Δ = 2402-4·(-5)·(-3)
Δ = 57540
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{57540}=\sqrt{4*14385}=\sqrt{4}*\sqrt{14385}=2\sqrt{14385}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-2\sqrt{14385}}{2*-5}=\frac{-240-2\sqrt{14385}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+2\sqrt{14385}}{2*-5}=\frac{-240+2\sqrt{14385}}{-10} $
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