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-7/8x-5/24x+1/3=-90
We move all terms to the left:
-7/8x-5/24x+1/3-(-90)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
Domain of the equation: 24x!=0We add all the numbers together, and all the variables
x!=0/24
x!=0
x∈R
-7/8x-5/24x+90+1/3=0
We calculate fractions
384x^2/1728x^2+(-1512x)/1728x^2+(-360x)/1728x^2+90=0
We multiply all the terms by the denominator
384x^2+(-1512x)+(-360x)+90*1728x^2=0
Wy multiply elements
384x^2+155520x^2+(-1512x)+(-360x)=0
We get rid of parentheses
384x^2+155520x^2-1512x-360x=0
We add all the numbers together, and all the variables
155904x^2-1872x=0
a = 155904; b = -1872; c = 0;
Δ = b2-4ac
Δ = -18722-4·155904·0
Δ = 3504384
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{3504384}=1872$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1872)-1872}{2*155904}=\frac{0}{311808} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1872)+1872}{2*155904}=\frac{3744}{311808} =39/3248 $
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