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(2x+1)(x+2)=77
We move all terms to the left:
(2x+1)(x+2)-(77)=0
We multiply parentheses ..
(+2x^2+4x+x+2)-77=0
We get rid of parentheses
2x^2+4x+x+2-77=0
We add all the numbers together, and all the variables
2x^2+5x-75=0
a = 2; b = 5; c = -75;
Δ = b2-4ac
Δ = 52-4·2·(-75)
Δ = 625
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{625}=25$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-25}{2*2}=\frac{-30}{4} =-7+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+25}{2*2}=\frac{20}{4} =5 $
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