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5x^2-x=23
We move all terms to the left:
5x^2-x-(23)=0
We add all the numbers together, and all the variables
5x^2-1x-23=0
a = 5; b = -1; c = -23;
Δ = b2-4ac
Δ = -12-4·5·(-23)
Δ = 461
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{461}}{2*5}=\frac{1-\sqrt{461}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{461}}{2*5}=\frac{1+\sqrt{461}}{10} $
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