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8^7-5x=2x^2-16x+9
We move all terms to the left:
8^7-5x-(2x^2-16x+9)=0
We add all the numbers together, and all the variables
-5x-(2x^2-16x+9)+2097152=0
We get rid of parentheses
-2x^2-5x+16x-9+2097152=0
We add all the numbers together, and all the variables
-2x^2+11x+2097143=0
a = -2; b = 11; c = +2097143;
Δ = b2-4ac
Δ = 112-4·(-2)·2097143
Δ = 16777265
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{-(11)-\sqrt{16777265}}{2*-2}=\frac{-11-\sqrt{16777265}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{16777265}}{2*-2}=\frac{-11+\sqrt{16777265}}{-4} $
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