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5(2x-9)(2x-9)+13=418
We move all terms to the left:
5(2x-9)(2x-9)+13-(418)=0
We add all the numbers together, and all the variables
5(2x-9)(2x-9)-405=0
We multiply parentheses ..
5(+4x^2-18x-18x+81)-405=0
We multiply parentheses
20x^2-90x-90x+405-405=0
We add all the numbers together, and all the variables
20x^2-180x=0
a = 20; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·20·0
Δ = 32400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{32400}=180$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*20}=\frac{0}{40} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*20}=\frac{360}{40} =9 $
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