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4x(2x+9)+(8x+3)+4x=180
We move all terms to the left:
4x(2x+9)+(8x+3)+4x-(180)=0
We add all the numbers together, and all the variables
4x+4x(2x+9)+(8x+3)-180=0
We multiply parentheses
8x^2+4x+36x+(8x+3)-180=0
We get rid of parentheses
8x^2+4x+36x+8x+3-180=0
We add all the numbers together, and all the variables
8x^2+48x-177=0
a = 8; b = 48; c = -177;
Δ = b2-4ac
Δ = 482-4·8·(-177)
Δ = 7968
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7968}=\sqrt{16*498}=\sqrt{16}*\sqrt{498}=4\sqrt{498}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{498}}{2*8}=\frac{-48-4\sqrt{498}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{498}}{2*8}=\frac{-48+4\sqrt{498}}{16} $
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