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-3(2x+13)=1/2x
We move all terms to the left:
-3(2x+13)-(1/2x)=0
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
-3(2x+13)-(+1/2x)=0
We multiply parentheses
-6x-(+1/2x)-39=0
We get rid of parentheses
-6x-1/2x-39=0
We multiply all the terms by the denominator
-6x*2x-39*2x-1=0
Wy multiply elements
-12x^2-78x-1=0
a = -12; b = -78; c = -1;
Δ = b2-4ac
Δ = -782-4·(-12)·(-1)
Δ = 6036
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6036}=\sqrt{4*1509}=\sqrt{4}*\sqrt{1509}=2\sqrt{1509}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1509}}{2*-12}=\frac{78-2\sqrt{1509}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1509}}{2*-12}=\frac{78+2\sqrt{1509}}{-24} $
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