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8+6(x-3)2x=13
We move all terms to the left:
8+6(x-3)2x-(13)=0
We add all the numbers together, and all the variables
6(x-3)2x-5=0
We multiply parentheses
12x^2-36x-5=0
a = 12; b = -36; c = -5;
Δ = b2-4ac
Δ = -362-4·12·(-5)
Δ = 1536
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-16\sqrt{6}}{2*12}=\frac{36-16\sqrt{6}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+16\sqrt{6}}{2*12}=\frac{36+16\sqrt{6}}{24} $
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