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5x(3x+13)=35
We move all terms to the left:
5x(3x+13)-(35)=0
We multiply parentheses
15x^2+65x-35=0
a = 15; b = 65; c = -35;
Δ = b2-4ac
Δ = 652-4·15·(-35)
Δ = 6325
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6325}=\sqrt{25*253}=\sqrt{25}*\sqrt{253}=5\sqrt{253}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-5\sqrt{253}}{2*15}=\frac{-65-5\sqrt{253}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+5\sqrt{253}}{2*15}=\frac{-65+5\sqrt{253}}{30} $
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