(2x+10)(x-5)=180

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Solution for (2x+10)(x-5)=180 equation:



(2x+10)(x-5)=180
We move all terms to the left:
(2x+10)(x-5)-(180)=0
We multiply parentheses ..
(+2x^2-10x+10x-50)-180=0
We get rid of parentheses
2x^2-10x+10x-50-180=0
We add all the numbers together, and all the variables
2x^2-230=0
a = 2; b = 0; c = -230;
Δ = b2-4ac
Δ = 02-4·2·(-230)
Δ = 1840
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:
$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{115}}{2*2}=\frac{0-4\sqrt{115}}{4} =-\frac{4\sqrt{115}}{4} =-\sqrt{115} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{115}}{2*2}=\frac{0+4\sqrt{115}}{4} =\frac{4\sqrt{115}}{4} =\sqrt{115} $

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