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5x(x+1)=50+4x
We move all terms to the left:
5x(x+1)-(50+4x)=0
We add all the numbers together, and all the variables
5x(x+1)-(4x+50)=0
We multiply parentheses
5x^2+5x-(4x+50)=0
We get rid of parentheses
5x^2+5x-4x-50=0
We add all the numbers together, and all the variables
5x^2+x-50=0
a = 5; b = 1; c = -50;
Δ = b2-4ac
Δ = 12-4·5·(-50)
Δ = 1001
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{-(1)-\sqrt{1001}}{2*5}=\frac{-1-\sqrt{1001}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1001}}{2*5}=\frac{-1+\sqrt{1001}}{10} $
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