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12x^2=18-4x
We move all terms to the left:
12x^2-(18-4x)=0
We add all the numbers together, and all the variables
12x^2-(-4x+18)=0
We get rid of parentheses
12x^2+4x-18=0
a = 12; b = 4; c = -18;
Δ = b2-4ac
Δ = 42-4·12·(-18)
Δ = 880
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{55}}{2*12}=\frac{-4-4\sqrt{55}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{55}}{2*12}=\frac{-4+4\sqrt{55}}{24} $
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