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15x^2-48x=9
We move all terms to the left:
15x^2-48x-(9)=0
a = 15; b = -48; c = -9;
Δ = b2-4ac
Δ = -482-4·15·(-9)
Δ = 2844
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2844}=\sqrt{36*79}=\sqrt{36}*\sqrt{79}=6\sqrt{79}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-6\sqrt{79}}{2*15}=\frac{48-6\sqrt{79}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+6\sqrt{79}}{2*15}=\frac{48+6\sqrt{79}}{30} $
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