(x+11)+(2x-3)+(2x+6)(2x+15)+(3x-19)+(3x-5)+(4x-9)+(5x)=360

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Solution for (x+11)+(2x-3)+(2x+6)(2x+15)+(3x-19)+(3x-5)+(4x-9)+(5x)=360 equation:



(x+11)+(2x-3)+(2x+6)(2x+15)+(3x-19)+(3x-5)+(4x-9)+(5x)=360
We move all terms to the left:
(x+11)+(2x-3)+(2x+6)(2x+15)+(3x-19)+(3x-5)+(4x-9)+(5x)-(360)=0
We add all the numbers together, and all the variables
5x+(x+11)+(2x-3)+(2x+6)(2x+15)+(3x-19)+(3x-5)+(4x-9)-360=0
We get rid of parentheses
5x+x+2x+(2x+6)(2x+15)+3x+3x+4x+11-3-19-5-9-360=0
We multiply parentheses ..
(+4x^2+30x+12x+90)+5x+x+2x+3x+3x+4x+11-3-19-5-9-360=0
We add all the numbers together, and all the variables
(+4x^2+30x+12x+90)+18x-385=0
We get rid of parentheses
4x^2+30x+12x+18x+90-385=0
We add all the numbers together, and all the variables
4x^2+60x-295=0
a = 4; b = 60; c = -295;
Δ = b2-4ac
Δ = 602-4·4·(-295)
Δ = 8320
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:
$\sqrt{\Delta}=\sqrt{8320}=\sqrt{64*130}=\sqrt{64}*\sqrt{130}=8\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-8\sqrt{130}}{2*4}=\frac{-60-8\sqrt{130}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+8\sqrt{130}}{2*4}=\frac{-60+8\sqrt{130}}{8} $

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