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5x(x-3)+2x=41
We move all terms to the left:
5x(x-3)+2x-(41)=0
We add all the numbers together, and all the variables
2x+5x(x-3)-41=0
We multiply parentheses
5x^2+2x-15x-41=0
We add all the numbers together, and all the variables
5x^2-13x-41=0
a = 5; b = -13; c = -41;
Δ = b2-4ac
Δ = -132-4·5·(-41)
Δ = 989
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{-(-13)-\sqrt{989}}{2*5}=\frac{13-\sqrt{989}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{989}}{2*5}=\frac{13+\sqrt{989}}{10} $
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