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3x(x-16)=136
We move all terms to the left:
3x(x-16)-(136)=0
We multiply parentheses
3x^2-48x-136=0
a = 3; b = -48; c = -136;
Δ = b2-4ac
Δ = -482-4·3·(-136)
Δ = 3936
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3936}=\sqrt{16*246}=\sqrt{16}*\sqrt{246}=4\sqrt{246}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{246}}{2*3}=\frac{48-4\sqrt{246}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{246}}{2*3}=\frac{48+4\sqrt{246}}{6} $
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