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8x^2-22x-21=112
We move all terms to the left:
8x^2-22x-21-(112)=0
We add all the numbers together, and all the variables
8x^2-22x-133=0
a = 8; b = -22; c = -133;
Δ = b2-4ac
Δ = -222-4·8·(-133)
Δ = 4740
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4740}=\sqrt{4*1185}=\sqrt{4}*\sqrt{1185}=2\sqrt{1185}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{1185}}{2*8}=\frac{22-2\sqrt{1185}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{1185}}{2*8}=\frac{22+2\sqrt{1185}}{16} $
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