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(2x-1)(x-3)=7-4x
We move all terms to the left:
(2x-1)(x-3)-(7-4x)=0
We add all the numbers together, and all the variables
(2x-1)(x-3)-(-4x+7)=0
We get rid of parentheses
(2x-1)(x-3)+4x-7=0
We multiply parentheses ..
(+2x^2-6x-1x+3)+4x-7=0
We get rid of parentheses
2x^2-6x-1x+4x+3-7=0
We add all the numbers together, and all the variables
2x^2-3x-4=0
a = 2; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·2·(-4)
Δ = 41
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{-(-3)-\sqrt{41}}{2*2}=\frac{3-\sqrt{41}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*2}=\frac{3+\sqrt{41}}{4} $
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