(4x-25)(2x-1)=180

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Solution for (4x-25)(2x-1)=180 equation:



(4x-25)(2x-1)=180
We move all terms to the left:
(4x-25)(2x-1)-(180)=0
We multiply parentheses ..
(+8x^2-4x-50x+25)-180=0
We get rid of parentheses
8x^2-4x-50x+25-180=0
We add all the numbers together, and all the variables
8x^2-54x-155=0
a = 8; b = -54; c = -155;
Δ = b2-4ac
Δ = -542-4·8·(-155)
Δ = 7876
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:
$\sqrt{\Delta}=\sqrt{7876}=\sqrt{4*1969}=\sqrt{4}*\sqrt{1969}=2\sqrt{1969}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{1969}}{2*8}=\frac{54-2\sqrt{1969}}{16} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{1969}}{2*8}=\frac{54+2\sqrt{1969}}{16} $

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