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5x(9x+40)+x=180
We move all terms to the left:
5x(9x+40)+x-(180)=0
We add all the numbers together, and all the variables
x+5x(9x+40)-180=0
We multiply parentheses
45x^2+x+200x-180=0
We add all the numbers together, and all the variables
45x^2+201x-180=0
a = 45; b = 201; c = -180;
Δ = b2-4ac
Δ = 2012-4·45·(-180)
Δ = 72801
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{72801}=\sqrt{9*8089}=\sqrt{9}*\sqrt{8089}=3\sqrt{8089}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(201)-3\sqrt{8089}}{2*45}=\frac{-201-3\sqrt{8089}}{90} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(201)+3\sqrt{8089}}{2*45}=\frac{-201+3\sqrt{8089}}{90} $
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