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15x(x+2)+9x=6
We move all terms to the left:
15x(x+2)+9x-(6)=0
We add all the numbers together, and all the variables
9x+15x(x+2)-6=0
We multiply parentheses
15x^2+9x+30x-6=0
We add all the numbers together, and all the variables
15x^2+39x-6=0
a = 15; b = 39; c = -6;
Δ = b2-4ac
Δ = 392-4·15·(-6)
Δ = 1881
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1881}=\sqrt{9*209}=\sqrt{9}*\sqrt{209}=3\sqrt{209}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{209}}{2*15}=\frac{-39-3\sqrt{209}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{209}}{2*15}=\frac{-39+3\sqrt{209}}{30} $
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