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(2x+1)(x-122)+37=360
We move all terms to the left:
(2x+1)(x-122)+37-(360)=0
We add all the numbers together, and all the variables
(2x+1)(x-122)-323=0
We multiply parentheses ..
(+2x^2-244x+x-122)-323=0
We get rid of parentheses
2x^2-244x+x-122-323=0
We add all the numbers together, and all the variables
2x^2-243x-445=0
a = 2; b = -243; c = -445;
Δ = b2-4ac
Δ = -2432-4·2·(-445)
Δ = 62609
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-243)-\sqrt{62609}}{2*2}=\frac{243-\sqrt{62609}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-243)+\sqrt{62609}}{2*2}=\frac{243+\sqrt{62609}}{4} $
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