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4x^2-57x+144=0
a = 4; b = -57; c = +144;
Δ = b2-4ac
Δ = -572-4·4·144
Δ = 945
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-3\sqrt{105}}{2*4}=\frac{57-3\sqrt{105}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+3\sqrt{105}}{2*4}=\frac{57+3\sqrt{105}}{8} $
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