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4x^2-72x+324=432
We move all terms to the left:
4x^2-72x+324-(432)=0
We add all the numbers together, and all the variables
4x^2-72x-108=0
a = 4; b = -72; c = -108;
Δ = b2-4ac
Δ = -722-4·4·(-108)
Δ = 6912
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-48\sqrt{3}}{2*4}=\frac{72-48\sqrt{3}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+48\sqrt{3}}{2*4}=\frac{72+48\sqrt{3}}{8} $
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