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x*x-x=187/288
We move all terms to the left:
x*x-x-(187/288)=0
We add all the numbers together, and all the variables
x*x-x-(+187/288)=0
We add all the numbers together, and all the variables
-1x+x*x-(+187/288)=0
Wy multiply elements
x^2-1x-(+187/288)=0
We get rid of parentheses
x^2-1x-187/288=0
We multiply all the terms by the denominator
x^2*288-1x*288-187=0
Wy multiply elements
288x^2-288x-187=0
a = 288; b = -288; c = -187;
Δ = b2-4ac
Δ = -2882-4·288·(-187)
Δ = 298368
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{298368}=\sqrt{576*518}=\sqrt{576}*\sqrt{518}=24\sqrt{518}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-24\sqrt{518}}{2*288}=\frac{288-24\sqrt{518}}{576} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+24\sqrt{518}}{2*288}=\frac{288+24\sqrt{518}}{576} $
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