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2/3X-3X=7
We move all terms to the left:
2/3X-3X-(7)=0
Domain of the equation: 3X!=0We add all the numbers together, and all the variables
X!=0/3
X!=0
X∈R
-3X+2/3X-7=0
We multiply all the terms by the denominator
-3X*3X-7*3X+2=0
Wy multiply elements
-9X^2-21X+2=0
a = -9; b = -21; c = +2;
Δ = b2-4ac
Δ = -212-4·(-9)·2
Δ = 513
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{57}}{2*-9}=\frac{21-3\sqrt{57}}{-18} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{57}}{2*-9}=\frac{21+3\sqrt{57}}{-18} $
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