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13x-9x+20=30x^2
We move all terms to the left:
13x-9x+20-(30x^2)=0
determiningTheFunctionDomain -30x^2+13x-9x+20=0
We add all the numbers together, and all the variables
-30x^2+4x+20=0
a = -30; b = 4; c = +20;
Δ = b2-4ac
Δ = 42-4·(-30)·20
Δ = 2416
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{151}}{2*-30}=\frac{-4-4\sqrt{151}}{-60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{151}}{2*-30}=\frac{-4+4\sqrt{151}}{-60} $
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