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2x(x+4)=-5x+1
We move all terms to the left:
2x(x+4)-(-5x+1)=0
We multiply parentheses
2x^2+8x-(-5x+1)=0
We get rid of parentheses
2x^2+8x+5x-1=0
We add all the numbers together, and all the variables
2x^2+13x-1=0
a = 2; b = 13; c = -1;
Δ = b2-4ac
Δ = 132-4·2·(-1)
Δ = 177
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{177}}{2*2}=\frac{-13-\sqrt{177}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{177}}{2*2}=\frac{-13+\sqrt{177}}{4} $
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