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2/3x-7=2x-19
We move all terms to the left:
2/3x-7-(2x-19)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
2/3x-2x+19-7=0
We multiply all the terms by the denominator
-2x*3x+19*3x-7*3x+2=0
Wy multiply elements
-6x^2+57x-21x+2=0
We add all the numbers together, and all the variables
-6x^2+36x+2=0
a = -6; b = 36; c = +2;
Δ = b2-4ac
Δ = 362-4·(-6)·2
Δ = 1344
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-8\sqrt{21}}{2*-6}=\frac{-36-8\sqrt{21}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+8\sqrt{21}}{2*-6}=\frac{-36+8\sqrt{21}}{-12} $
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