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4x^2-46x+130=0
a = 4; b = -46; c = +130;
Δ = b2-4ac
Δ = -462-4·4·130
Δ = 36
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{36}=6$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-6}{2*4}=\frac{40}{8} =5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+6}{2*4}=\frac{52}{8} =6+1/2 $
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