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1/4x+10=1x+54
We move all terms to the left:
1/4x+10-(1x+54)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
1/4x-(x+54)+10=0
We get rid of parentheses
1/4x-x-54+10=0
We multiply all the terms by the denominator
-x*4x-54*4x+10*4x+1=0
Wy multiply elements
-4x^2-216x+40x+1=0
We add all the numbers together, and all the variables
-4x^2-176x+1=0
a = -4; b = -176; c = +1;
Δ = b2-4ac
Δ = -1762-4·(-4)·1
Δ = 30992
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{30992}=\sqrt{16*1937}=\sqrt{16}*\sqrt{1937}=4\sqrt{1937}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-4\sqrt{1937}}{2*-4}=\frac{176-4\sqrt{1937}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+4\sqrt{1937}}{2*-4}=\frac{176+4\sqrt{1937}}{-8} $
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