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4x(12-x)=14
We move all terms to the left:
4x(12-x)-(14)=0
We add all the numbers together, and all the variables
4x(-1x+12)-14=0
We multiply parentheses
-4x^2+48x-14=0
a = -4; b = 48; c = -14;
Δ = b2-4ac
Δ = 482-4·(-4)·(-14)
Δ = 2080
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2080}=\sqrt{16*130}=\sqrt{16}*\sqrt{130}=4\sqrt{130}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{130}}{2*-4}=\frac{-48-4\sqrt{130}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{130}}{2*-4}=\frac{-48+4\sqrt{130}}{-8} $
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