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-4/3x+30=-3x+45
We move all terms to the left:
-4/3x+30-(-3x+45)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
-4/3x+3x-45+30=0
We multiply all the terms by the denominator
3x*3x-45*3x+30*3x-4=0
Wy multiply elements
9x^2-135x+90x-4=0
We add all the numbers together, and all the variables
9x^2-45x-4=0
a = 9; b = -45; c = -4;
Δ = b2-4ac
Δ = -452-4·9·(-4)
Δ = 2169
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2169}=\sqrt{9*241}=\sqrt{9}*\sqrt{241}=3\sqrt{241}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{241}}{2*9}=\frac{45-3\sqrt{241}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{241}}{2*9}=\frac{45+3\sqrt{241}}{18} $
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