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(2x-6)(x-4)=2x+3x-7
We move all terms to the left:
(2x-6)(x-4)-(2x+3x-7)=0
We add all the numbers together, and all the variables
(2x-6)(x-4)-(5x-7)=0
We get rid of parentheses
(2x-6)(x-4)-5x+7=0
We multiply parentheses ..
(+2x^2-8x-6x+24)-5x+7=0
We get rid of parentheses
2x^2-8x-6x-5x+24+7=0
We add all the numbers together, and all the variables
2x^2-19x+31=0
a = 2; b = -19; c = +31;
Δ = b2-4ac
Δ = -192-4·2·31
Δ = 113
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{113}}{2*2}=\frac{19-\sqrt{113}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{113}}{2*2}=\frac{19+\sqrt{113}}{4} $
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