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(-7+8x)(-7+8x)=5
We move all terms to the left:
(-7+8x)(-7+8x)-(5)=0
We add all the numbers together, and all the variables
(8x-7)(8x-7)-5=0
We multiply parentheses ..
(+64x^2-56x-56x+49)-5=0
We get rid of parentheses
64x^2-56x-56x+49-5=0
We add all the numbers together, and all the variables
64x^2-112x+44=0
a = 64; b = -112; c = +44;
Δ = b2-4ac
Δ = -1122-4·64·44
Δ = 1280
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-16\sqrt{5}}{2*64}=\frac{112-16\sqrt{5}}{128} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+16\sqrt{5}}{2*64}=\frac{112+16\sqrt{5}}{128} $
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