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(1/4x)+x+(x-81)=180
We move all terms to the left:
(1/4x)+x+(x-81)-(180)=0
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+1/4x)+x+(x-81)-180=0
We add all the numbers together, and all the variables
x+(+1/4x)+(x-81)-180=0
We get rid of parentheses
x+1/4x+x-81-180=0
We multiply all the terms by the denominator
x*4x+x*4x-81*4x-180*4x+1=0
Wy multiply elements
4x^2+4x^2-324x-720x+1=0
We add all the numbers together, and all the variables
8x^2-1044x+1=0
a = 8; b = -1044; c = +1;
Δ = b2-4ac
Δ = -10442-4·8·1
Δ = 1089904
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1089904}=\sqrt{16*68119}=\sqrt{16}*\sqrt{68119}=4\sqrt{68119}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1044)-4\sqrt{68119}}{2*8}=\frac{1044-4\sqrt{68119}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1044)+4\sqrt{68119}}{2*8}=\frac{1044+4\sqrt{68119}}{16} $
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