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4x(x+9)=12
We move all terms to the left:
4x(x+9)-(12)=0
We multiply parentheses
4x^2+36x-12=0
a = 4; b = 36; c = -12;
Δ = b2-4ac
Δ = 362-4·4·(-12)
Δ = 1488
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{93}}{2*4}=\frac{-36-4\sqrt{93}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{93}}{2*4}=\frac{-36+4\sqrt{93}}{8} $
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