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4x^2-6x+9=369
We move all terms to the left:
4x^2-6x+9-(369)=0
We add all the numbers together, and all the variables
4x^2-6x-360=0
a = 4; b = -6; c = -360;
Δ = b2-4ac
Δ = -62-4·4·(-360)
Δ = 5796
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5796}=\sqrt{36*161}=\sqrt{36}*\sqrt{161}=6\sqrt{161}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{161}}{2*4}=\frac{6-6\sqrt{161}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{161}}{2*4}=\frac{6+6\sqrt{161}}{8} $
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