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x(10x+1)=82
We move all terms to the left:
x(10x+1)-(82)=0
We multiply parentheses
10x^2+x-82=0
a = 10; b = 1; c = -82;
Δ = b2-4ac
Δ = 12-4·10·(-82)
Δ = 3281
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{3281}}{2*10}=\frac{-1-\sqrt{3281}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{3281}}{2*10}=\frac{-1+\sqrt{3281}}{20} $
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