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8x^2-24x-21=x
We move all terms to the left:
8x^2-24x-21-(x)=0
We add all the numbers together, and all the variables
8x^2-25x-21=0
a = 8; b = -25; c = -21;
Δ = b2-4ac
Δ = -252-4·8·(-21)
Δ = 1297
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{-(-25)-\sqrt{1297}}{2*8}=\frac{25-\sqrt{1297}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{1297}}{2*8}=\frac{25+\sqrt{1297}}{16} $
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