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4x^2-180x+1600=0
a = 4; b = -180; c = +1600;
Δ = b2-4ac
Δ = -1802-4·4·1600
Δ = 6800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6800}=\sqrt{400*17}=\sqrt{400}*\sqrt{17}=20\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-20\sqrt{17}}{2*4}=\frac{180-20\sqrt{17}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+20\sqrt{17}}{2*4}=\frac{180+20\sqrt{17}}{8} $
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