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(3/2)(2x+6)=3x+9
We move all terms to the left:
(3/2)(2x+6)-(3x+9)=0
Domain of the equation: 2)(2x+6)!=0We add all the numbers together, and all the variables
x∈R
(+3/2)(2x+6)-(3x+9)=0
We get rid of parentheses
(+3/2)(2x+6)-3x-9=0
We multiply parentheses ..
(+6x^2+3/2*6)-3x-9=0
We multiply all the terms by the denominator
(+6x^2+3-3x*2*6)-9*2*6)=0
We add all the numbers together, and all the variables
(+6x^2+3-3x*2*6)=0
We get rid of parentheses
6x^2-3x*2*6+3=0
Wy multiply elements
6x^2-36x*6+3=0
Wy multiply elements
6x^2-216x+3=0
a = 6; b = -216; c = +3;
Δ = b2-4ac
Δ = -2162-4·6·3
Δ = 46584
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{46584}=\sqrt{36*1294}=\sqrt{36}*\sqrt{1294}=6\sqrt{1294}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-6\sqrt{1294}}{2*6}=\frac{216-6\sqrt{1294}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+6\sqrt{1294}}{2*6}=\frac{216+6\sqrt{1294}}{12} $
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