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6x=-3/2x-17
We move all terms to the left:
6x-(-3/2x-17)=0
Domain of the equation: 2x-17)!=0We get rid of parentheses
x∈R
6x+3/2x+17=0
We multiply all the terms by the denominator
6x*2x+17*2x+3=0
Wy multiply elements
12x^2+34x+3=0
a = 12; b = 34; c = +3;
Δ = b2-4ac
Δ = 342-4·12·3
Δ = 1012
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1012}=\sqrt{4*253}=\sqrt{4}*\sqrt{253}=2\sqrt{253}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{253}}{2*12}=\frac{-34-2\sqrt{253}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{253}}{2*12}=\frac{-34+2\sqrt{253}}{24} $
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