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3(2x-9)5x=-41
We move all terms to the left:
3(2x-9)5x-(-41)=0
We add all the numbers together, and all the variables
3(2x-9)5x+41=0
We multiply parentheses
30x^2-135x+41=0
a = 30; b = -135; c = +41;
Δ = b2-4ac
Δ = -1352-4·30·41
Δ = 13305
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{-(-135)-\sqrt{13305}}{2*30}=\frac{135-\sqrt{13305}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+\sqrt{13305}}{2*30}=\frac{135+\sqrt{13305}}{60} $
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