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10+24x-6x^2=x
We move all terms to the left:
10+24x-6x^2-(x)=0
We add all the numbers together, and all the variables
-6x^2+23x+10=0
a = -6; b = 23; c = +10;
Δ = b2-4ac
Δ = 232-4·(-6)·10
Δ = 769
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{769}}{2*-6}=\frac{-23-\sqrt{769}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{769}}{2*-6}=\frac{-23+\sqrt{769}}{-12} $
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