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(5x-2)(x+1)=1
We move all terms to the left:
(5x-2)(x+1)-(1)=0
We multiply parentheses ..
(+5x^2+5x-2x-2)-1=0
We get rid of parentheses
5x^2+5x-2x-2-1=0
We add all the numbers together, and all the variables
5x^2+3x-3=0
a = 5; b = 3; c = -3;
Δ = b2-4ac
Δ = 32-4·5·(-3)
Δ = 69
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{69}}{2*5}=\frac{-3-\sqrt{69}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{69}}{2*5}=\frac{-3+\sqrt{69}}{10} $
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