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2x+7=1/3x+5
We move all terms to the left:
2x+7-(1/3x+5)=0
Domain of the equation: 3x+5)!=0We get rid of parentheses
x∈R
2x-1/3x-5+7=0
We multiply all the terms by the denominator
2x*3x-5*3x+7*3x-1=0
Wy multiply elements
6x^2-15x+21x-1=0
We add all the numbers together, and all the variables
6x^2+6x-1=0
a = 6; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·6·(-1)
Δ = 60
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{15}}{2*6}=\frac{-6-2\sqrt{15}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*6}=\frac{-6+2\sqrt{15}}{12} $
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