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(2x-5)(x-7)=2
We move all terms to the left:
(2x-5)(x-7)-(2)=0
We multiply parentheses ..
(+2x^2-14x-5x+35)-2=0
We get rid of parentheses
2x^2-14x-5x+35-2=0
We add all the numbers together, and all the variables
2x^2-19x+33=0
a = 2; b = -19; c = +33;
Δ = b2-4ac
Δ = -192-4·2·33
Δ = 97
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{-(-19)-\sqrt{97}}{2*2}=\frac{19-\sqrt{97}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{97}}{2*2}=\frac{19+\sqrt{97}}{4} $
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