(5x-2)(3x+4)=180

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Solution for (5x-2)(3x+4)=180 equation:



(5x-2)(3x+4)=180
We move all terms to the left:
(5x-2)(3x+4)-(180)=0
We multiply parentheses ..
(+15x^2+20x-6x-8)-180=0
We get rid of parentheses
15x^2+20x-6x-8-180=0
We add all the numbers together, and all the variables
15x^2+14x-188=0
a = 15; b = 14; c = -188;
Δ = b2-4ac
Δ = 142-4·15·(-188)
Δ = 11476
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:
$\sqrt{\Delta}=\sqrt{11476}=\sqrt{4*2869}=\sqrt{4}*\sqrt{2869}=2\sqrt{2869}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{2869}}{2*15}=\frac{-14-2\sqrt{2869}}{30} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{2869}}{2*15}=\frac{-14+2\sqrt{2869}}{30} $

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