(4x-13)(x+44)=180

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Solution for (4x-13)(x+44)=180 equation:



(4x-13)(x+44)=180
We move all terms to the left:
(4x-13)(x+44)-(180)=0
We multiply parentheses ..
(+4x^2+176x-13x-572)-180=0
We get rid of parentheses
4x^2+176x-13x-572-180=0
We add all the numbers together, and all the variables
4x^2+163x-752=0
a = 4; b = 163; c = -752;
Δ = b2-4ac
Δ = 1632-4·4·(-752)
Δ = 38601
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:
$\sqrt{\Delta}=\sqrt{38601}=\sqrt{9*4289}=\sqrt{9}*\sqrt{4289}=3\sqrt{4289}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(163)-3\sqrt{4289}}{2*4}=\frac{-163-3\sqrt{4289}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(163)+3\sqrt{4289}}{2*4}=\frac{-163+3\sqrt{4289}}{8} $

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