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2x(x+24)=192
We move all terms to the left:
2x(x+24)-(192)=0
We multiply parentheses
2x^2+48x-192=0
a = 2; b = 48; c = -192;
Δ = b2-4ac
Δ = 482-4·2·(-192)
Δ = 3840
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-16\sqrt{15}}{2*2}=\frac{-48-16\sqrt{15}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+16\sqrt{15}}{2*2}=\frac{-48+16\sqrt{15}}{4} $
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