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(2x-1)(x+3)=14
We move all terms to the left:
(2x-1)(x+3)-(14)=0
We multiply parentheses ..
(+2x^2+6x-1x-3)-14=0
We get rid of parentheses
2x^2+6x-1x-3-14=0
We add all the numbers together, and all the variables
2x^2+5x-17=0
a = 2; b = 5; c = -17;
Δ = b2-4ac
Δ = 52-4·2·(-17)
Δ = 161
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{-(5)-\sqrt{161}}{2*2}=\frac{-5-\sqrt{161}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{161}}{2*2}=\frac{-5+\sqrt{161}}{4} $
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