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2x^2+46x+2000=266x
We move all terms to the left:
2x^2+46x+2000-(266x)=0
We add all the numbers together, and all the variables
2x^2-220x+2000=0
a = 2; b = -220; c = +2000;
Δ = b2-4ac
Δ = -2202-4·2·2000
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-220)-180}{2*2}=\frac{40}{4} =10 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-220)+180}{2*2}=\frac{400}{4} =100 $
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