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2x+3x(3x+4)=180
We move all terms to the left:
2x+3x(3x+4)-(180)=0
We multiply parentheses
9x^2+2x+12x-180=0
We add all the numbers together, and all the variables
9x^2+14x-180=0
a = 9; b = 14; c = -180;
Δ = b2-4ac
Δ = 142-4·9·(-180)
Δ = 6676
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6676}=\sqrt{4*1669}=\sqrt{4}*\sqrt{1669}=2\sqrt{1669}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{1669}}{2*9}=\frac{-14-2\sqrt{1669}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{1669}}{2*9}=\frac{-14+2\sqrt{1669}}{18} $
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