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(0.5x-18)-(24+1/3x)=-15
We move all terms to the left:
(0.5x-18)-(24+1/3x)-(-15)=0
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(0.5x-18)-(1/3x+24)-(-15)=0
We add all the numbers together, and all the variables
(0.5x-18)-(1/3x+24)+15=0
We get rid of parentheses
0.5x-1/3x-18-24+15=0
We multiply all the terms by the denominator
(0.5x)*3x-18*3x-24*3x+15*3x-1=0
We add all the numbers together, and all the variables
(+0.5x)*3x-18*3x-24*3x+15*3x-1=0
We multiply parentheses
0x^2-18*3x-24*3x+15*3x-1=0
Wy multiply elements
0x^2-54x-72x+45x-1=0
We add all the numbers together, and all the variables
x^2-81x-1=0
a = 1; b = -81; c = -1;
Δ = b2-4ac
Δ = -812-4·1·(-1)
Δ = 6565
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-\sqrt{6565}}{2*1}=\frac{81-\sqrt{6565}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+\sqrt{6565}}{2*1}=\frac{81+\sqrt{6565}}{2} $
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