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x+x*1.5x=560
We move all terms to the left:
x+x*1.5x-(560)=0
Wy multiply elements
x^2+x-560=0
a = 1; b = 1; c = -560;
Δ = b2-4ac
Δ = 12-4·1·(-560)
Δ = 2241
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2241}=\sqrt{9*249}=\sqrt{9}*\sqrt{249}=3\sqrt{249}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{249}}{2*1}=\frac{-1-3\sqrt{249}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{249}}{2*1}=\frac{-1+3\sqrt{249}}{2} $
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