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4200=4x^2+6x+12
We move all terms to the left:
4200-(4x^2+6x+12)=0
We get rid of parentheses
-4x^2-6x-12+4200=0
We add all the numbers together, and all the variables
-4x^2-6x+4188=0
a = -4; b = -6; c = +4188;
Δ = b2-4ac
Δ = -62-4·(-4)·4188
Δ = 67044
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{67044}=\sqrt{4*16761}=\sqrt{4}*\sqrt{16761}=2\sqrt{16761}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{16761}}{2*-4}=\frac{6-2\sqrt{16761}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{16761}}{2*-4}=\frac{6+2\sqrt{16761}}{-8} $
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