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4x^2+108x+454=0
a = 4; b = 108; c = +454;
Δ = b2-4ac
Δ = 1082-4·4·454
Δ = 4400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4400}=\sqrt{400*11}=\sqrt{400}*\sqrt{11}=20\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-20\sqrt{11}}{2*4}=\frac{-108-20\sqrt{11}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+20\sqrt{11}}{2*4}=\frac{-108+20\sqrt{11}}{8} $
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