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420000=4x^2+6x+12
We move all terms to the left:
420000-(4x^2+6x+12)=0
We get rid of parentheses
-4x^2-6x-12+420000=0
We add all the numbers together, and all the variables
-4x^2-6x+419988=0
a = -4; b = -6; c = +419988;
Δ = b2-4ac
Δ = -62-4·(-4)·419988
Δ = 6719844
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6719844}=\sqrt{4*1679961}=\sqrt{4}*\sqrt{1679961}=2\sqrt{1679961}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{1679961}}{2*-4}=\frac{6-2\sqrt{1679961}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{1679961}}{2*-4}=\frac{6+2\sqrt{1679961}}{-8} $
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