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1/2x-3(1/2x+5)=-1/2x+9
We move all terms to the left:
1/2x-3(1/2x+5)-(-1/2x+9)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 2x+5)!=0
x∈R
Domain of the equation: 2x+9)!=0We multiply parentheses
x∈R
1/2x-3x-(-1/2x+9)-15=0
We get rid of parentheses
1/2x-3x+1/2x-9-15=0
We multiply all the terms by the denominator
-3x*2x-9*2x-15*2x+1+1=0
We add all the numbers together, and all the variables
-3x*2x-9*2x-15*2x+2=0
Wy multiply elements
-6x^2-18x-30x+2=0
We add all the numbers together, and all the variables
-6x^2-48x+2=0
a = -6; b = -48; c = +2;
Δ = b2-4ac
Δ = -482-4·(-6)·2
Δ = 2352
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-28\sqrt{3}}{2*-6}=\frac{48-28\sqrt{3}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+28\sqrt{3}}{2*-6}=\frac{48+28\sqrt{3}}{-12} $
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