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X-15=1/4X
We move all terms to the left:
X-15-(1/4X)=0
Domain of the equation: 4X)!=0We add all the numbers together, and all the variables
X!=0/1
X!=0
X∈R
X-(+1/4X)-15=0
We get rid of parentheses
X-1/4X-15=0
We multiply all the terms by the denominator
X*4X-15*4X-1=0
Wy multiply elements
4X^2-60X-1=0
a = 4; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·4·(-1)
Δ = 3616
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{226}}{2*4}=\frac{60-4\sqrt{226}}{8} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{226}}{2*4}=\frac{60+4\sqrt{226}}{8} $
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