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-1/3x+15=-x+5
We move all terms to the left:
-1/3x+15-(-x+5)=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+5)+15=0
We get rid of parentheses
-1/3x+1x-5+15=0
We multiply all the terms by the denominator
1x*3x-5*3x+15*3x-1=0
Wy multiply elements
3x^2-15x+45x-1=0
We add all the numbers together, and all the variables
3x^2+30x-1=0
a = 3; b = 30; c = -1;
Δ = b2-4ac
Δ = 302-4·3·(-1)
Δ = 912
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-4\sqrt{57}}{2*3}=\frac{-30-4\sqrt{57}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+4\sqrt{57}}{2*3}=\frac{-30+4\sqrt{57}}{6} $
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