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/5x-24=11-2x
We move all terms to the left:
/5x-24-(11-2x)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
/5x-(-2x+11)-24=0
We get rid of parentheses
/5x+2x-11-24=0
We multiply all the terms by the denominator
2x*5x-11*5x-24*5x+=0
We add all the numbers together, and all the variables
2x*5x-11*5x-24*5x=0
Wy multiply elements
10x^2-55x-120x=0
We add all the numbers together, and all the variables
10x^2-175x=0
a = 10; b = -175; c = 0;
Δ = b2-4ac
Δ = -1752-4·10·0
Δ = 30625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{30625}=175$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-175)-175}{2*10}=\frac{0}{20} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-175)+175}{2*10}=\frac{350}{20} =17+1/2 $
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