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2/3x+3=-5x-65
We move all terms to the left:
2/3x+3-(-5x-65)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
2/3x+5x+65+3=0
We multiply all the terms by the denominator
5x*3x+65*3x+3*3x+2=0
Wy multiply elements
15x^2+195x+9x+2=0
We add all the numbers together, and all the variables
15x^2+204x+2=0
a = 15; b = 204; c = +2;
Δ = b2-4ac
Δ = 2042-4·15·2
Δ = 41496
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{41496}=\sqrt{4*10374}=\sqrt{4}*\sqrt{10374}=2\sqrt{10374}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(204)-2\sqrt{10374}}{2*15}=\frac{-204-2\sqrt{10374}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(204)+2\sqrt{10374}}{2*15}=\frac{-204+2\sqrt{10374}}{30} $
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