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2x^2=+3x+1
We move all terms to the left:
2x^2-(+3x+1)=0
We add all the numbers together, and all the variables
2x^2-(3x+1)=0
We get rid of parentheses
2x^2-3x-1=0
a = 2; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·2·(-1)
Δ = 17
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{17}}{2*2}=\frac{3-\sqrt{17}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{17}}{2*2}=\frac{3+\sqrt{17}}{4} $
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