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-1/3x+24=-x+8
We move all terms to the left:
-1/3x+24-(-x+8)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-1/3x-(-1x+8)+24=0
We get rid of parentheses
-1/3x+1x-8+24=0
We multiply all the terms by the denominator
1x*3x-8*3x+24*3x-1=0
Wy multiply elements
3x^2-24x+72x-1=0
We add all the numbers together, and all the variables
3x^2+48x-1=0
a = 3; b = 48; c = -1;
Δ = b2-4ac
Δ = 482-4·3·(-1)
Δ = 2316
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2316}=\sqrt{4*579}=\sqrt{4}*\sqrt{579}=2\sqrt{579}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{579}}{2*3}=\frac{-48-2\sqrt{579}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{579}}{2*3}=\frac{-48+2\sqrt{579}}{6} $
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