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x(6x+76)=6432
We move all terms to the left:
x(6x+76)-(6432)=0
We multiply parentheses
6x^2+76x-6432=0
a = 6; b = 76; c = -6432;
Δ = b2-4ac
Δ = 762-4·6·(-6432)
Δ = 160144
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{160144}=\sqrt{16*10009}=\sqrt{16}*\sqrt{10009}=4\sqrt{10009}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-4\sqrt{10009}}{2*6}=\frac{-76-4\sqrt{10009}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+4\sqrt{10009}}{2*6}=\frac{-76+4\sqrt{10009}}{12} $
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