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(2x+3)(x-2)=22
We move all terms to the left:
(2x+3)(x-2)-(22)=0
We multiply parentheses ..
(+2x^2-4x+3x-6)-22=0
We get rid of parentheses
2x^2-4x+3x-6-22=0
We add all the numbers together, and all the variables
2x^2-1x-28=0
a = 2; b = -1; c = -28;
Δ = b2-4ac
Δ = -12-4·2·(-28)
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-15}{2*2}=\frac{-14}{4} =-3+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+15}{2*2}=\frac{16}{4} =4 $
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