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15X(X+8)=5
We move all terms to the left:
15X(X+8)-(5)=0
We multiply parentheses
15X^2+120X-5=0
a = 15; b = 120; c = -5;
Δ = b2-4ac
Δ = 1202-4·15·(-5)
Δ = 14700
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14700}=\sqrt{4900*3}=\sqrt{4900}*\sqrt{3}=70\sqrt{3}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-70\sqrt{3}}{2*15}=\frac{-120-70\sqrt{3}}{30} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+70\sqrt{3}}{2*15}=\frac{-120+70\sqrt{3}}{30} $
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