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2.5x+17=-2/3x-21
We move all terms to the left:
2.5x+17-(-2/3x-21)=0
Domain of the equation: 3x-21)!=0We get rid of parentheses
x∈R
2.5x+2/3x+21+17=0
We multiply all the terms by the denominator
(2.5x)*3x+21*3x+17*3x+2=0
We add all the numbers together, and all the variables
(+2.5x)*3x+21*3x+17*3x+2=0
We multiply parentheses
6x^2+21*3x+17*3x+2=0
Wy multiply elements
6x^2+63x+51x+2=0
We add all the numbers together, and all the variables
6x^2+114x+2=0
a = 6; b = 114; c = +2;
Δ = b2-4ac
Δ = 1142-4·6·2
Δ = 12948
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12948}=\sqrt{4*3237}=\sqrt{4}*\sqrt{3237}=2\sqrt{3237}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-2\sqrt{3237}}{2*6}=\frac{-114-2\sqrt{3237}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+2\sqrt{3237}}{2*6}=\frac{-114+2\sqrt{3237}}{12} $
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