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x(5x+x)=x^2+3x+1
We move all terms to the left:
x(5x+x)-(x^2+3x+1)=0
We add all the numbers together, and all the variables
x(+6x)-(x^2+3x+1)=0
We multiply parentheses
6x^2-(x^2+3x+1)=0
We get rid of parentheses
6x^2-x^2-3x-1=0
We add all the numbers together, and all the variables
5x^2-3x-1=0
a = 5; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·5·(-1)
Δ = 29
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{-(-3)-\sqrt{29}}{2*5}=\frac{3-\sqrt{29}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{29}}{2*5}=\frac{3+\sqrt{29}}{10} $
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