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4x^2+288x+36=0
a = 4; b = 288; c = +36;
Δ = b2-4ac
Δ = 2882-4·4·36
Δ = 82368
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{82368}=\sqrt{576*143}=\sqrt{576}*\sqrt{143}=24\sqrt{143}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-24\sqrt{143}}{2*4}=\frac{-288-24\sqrt{143}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+24\sqrt{143}}{2*4}=\frac{-288+24\sqrt{143}}{8} $
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