(5x-10)(4x+11)=180

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Solution for (5x-10)(4x+11)=180 equation:



(5x-10)(4x+11)=180
We move all terms to the left:
(5x-10)(4x+11)-(180)=0
We multiply parentheses ..
(+20x^2+55x-40x-110)-180=0
We get rid of parentheses
20x^2+55x-40x-110-180=0
We add all the numbers together, and all the variables
20x^2+15x-290=0
a = 20; b = 15; c = -290;
Δ = b2-4ac
Δ = 152-4·20·(-290)
Δ = 23425
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:
$\sqrt{\Delta}=\sqrt{23425}=\sqrt{25*937}=\sqrt{25}*\sqrt{937}=5\sqrt{937}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{937}}{2*20}=\frac{-15-5\sqrt{937}}{40} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{937}}{2*20}=\frac{-15+5\sqrt{937}}{40} $

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