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2/3x+6-10x=30
We move all terms to the left:
2/3x+6-10x-(30)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-10x+2/3x-24=0
We multiply all the terms by the denominator
-10x*3x-24*3x+2=0
Wy multiply elements
-30x^2-72x+2=0
a = -30; b = -72; c = +2;
Δ = b2-4ac
Δ = -722-4·(-30)·2
Δ = 5424
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5424}=\sqrt{16*339}=\sqrt{16}*\sqrt{339}=4\sqrt{339}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{339}}{2*-30}=\frac{72-4\sqrt{339}}{-60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{339}}{2*-30}=\frac{72+4\sqrt{339}}{-60} $
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