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3x(16-x)=136
We move all terms to the left:
3x(16-x)-(136)=0
We add all the numbers together, and all the variables
3x(-1x+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 = 672
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{42}}{2*-3}=\frac{-48-4\sqrt{42}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{42}}{2*-3}=\frac{-48+4\sqrt{42}}{-6} $
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