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X(676-X)=576
We move all terms to the left:
X(676-X)-(576)=0
We add all the numbers together, and all the variables
X(-1X+676)-576=0
We multiply parentheses
-1X^2+676X-576=0
a = -1; b = 676; c = -576;
Δ = b2-4ac
Δ = 6762-4·(-1)·(-576)
Δ = 454672
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{454672}=\sqrt{16*28417}=\sqrt{16}*\sqrt{28417}=4\sqrt{28417}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(676)-4\sqrt{28417}}{2*-1}=\frac{-676-4\sqrt{28417}}{-2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(676)+4\sqrt{28417}}{2*-1}=\frac{-676+4\sqrt{28417}}{-2} $
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