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3x+17+(1/2x-5)=180
We move all terms to the left:
3x+17+(1/2x-5)-(180)=0
Domain of the equation: 2x-5)!=0We add all the numbers together, and all the variables
x∈R
3x+(1/2x-5)-163=0
We get rid of parentheses
3x+1/2x-5-163=0
We multiply all the terms by the denominator
3x*2x-5*2x-163*2x+1=0
Wy multiply elements
6x^2-10x-326x+1=0
We add all the numbers together, and all the variables
6x^2-336x+1=0
a = 6; b = -336; c = +1;
Δ = b2-4ac
Δ = -3362-4·6·1
Δ = 112872
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{112872}=\sqrt{4*28218}=\sqrt{4}*\sqrt{28218}=2\sqrt{28218}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-336)-2\sqrt{28218}}{2*6}=\frac{336-2\sqrt{28218}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-336)+2\sqrt{28218}}{2*6}=\frac{336+2\sqrt{28218}}{12} $
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