15x(x+7)=240

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Solution for 15x(x+7)=240 equation:



15x(x+7)=240
We move all terms to the left:
15x(x+7)-(240)=0
We multiply parentheses
15x^2+105x-240=0
a = 15; b = 105; c = -240;
Δ = b2-4ac
Δ = 1052-4·15·(-240)
Δ = 25425
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:
$\sqrt{\Delta}=\sqrt{25425}=\sqrt{225*113}=\sqrt{225}*\sqrt{113}=15\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-15\sqrt{113}}{2*15}=\frac{-105-15\sqrt{113}}{30} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+15\sqrt{113}}{2*15}=\frac{-105+15\sqrt{113}}{30} $

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