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x+3=1/4x+6
We move all terms to the left:
x+3-(1/4x+6)=0
Domain of the equation: 4x+6)!=0We get rid of parentheses
x∈R
x-1/4x-6+3=0
We multiply all the terms by the denominator
x*4x-6*4x+3*4x-1=0
Wy multiply elements
4x^2-24x+12x-1=0
We add all the numbers together, and all the variables
4x^2-12x-1=0
a = 4; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·4·(-1)
Δ = 160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{10}}{2*4}=\frac{12-4\sqrt{10}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{10}}{2*4}=\frac{12+4\sqrt{10}}{8} $
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