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5x(2x-9)=46
We move all terms to the left:
5x(2x-9)-(46)=0
We multiply parentheses
10x^2-45x-46=0
a = 10; b = -45; c = -46;
Δ = b2-4ac
Δ = -452-4·10·(-46)
Δ = 3865
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{-(-45)-\sqrt{3865}}{2*10}=\frac{45-\sqrt{3865}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{3865}}{2*10}=\frac{45+\sqrt{3865}}{20} $
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