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5x(3x-1)=46
We move all terms to the left:
5x(3x-1)-(46)=0
We multiply parentheses
15x^2-5x-46=0
a = 15; b = -5; c = -46;
Δ = b2-4ac
Δ = -52-4·15·(-46)
Δ = 2785
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{2785}}{2*15}=\frac{5-\sqrt{2785}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{2785}}{2*15}=\frac{5+\sqrt{2785}}{30} $
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