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4x^2-80x+279=253
We move all terms to the left:
4x^2-80x+279-(253)=0
We add all the numbers together, and all the variables
4x^2-80x+26=0
a = 4; b = -80; c = +26;
Δ = b2-4ac
Δ = -802-4·4·26
Δ = 5984
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5984}=\sqrt{16*374}=\sqrt{16}*\sqrt{374}=4\sqrt{374}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{374}}{2*4}=\frac{80-4\sqrt{374}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{374}}{2*4}=\frac{80+4\sqrt{374}}{8} $
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