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4(3x^2-46x+130)=0
We multiply parentheses
12x^2-184x+520=0
a = 12; b = -184; c = +520;
Δ = b2-4ac
Δ = -1842-4·12·520
Δ = 8896
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8896}=\sqrt{64*139}=\sqrt{64}*\sqrt{139}=8\sqrt{139}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-184)-8\sqrt{139}}{2*12}=\frac{184-8\sqrt{139}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-184)+8\sqrt{139}}{2*12}=\frac{184+8\sqrt{139}}{24} $
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