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(5x-3)(3-x)=(3-x)(4x-7)
We move all terms to the left:
(5x-3)(3-x)-((3-x)(4x-7))=0
We add all the numbers together, and all the variables
(5x-3)(-1x+3)-((-1x+3)(4x-7))=0
We multiply parentheses ..
(-5x^2+15x+3x-9)-((-1x+3)(4x-7))=0
We calculate terms in parentheses: -((-1x+3)(4x-7)), so:We get rid of parentheses
(-1x+3)(4x-7)
We multiply parentheses ..
(-4x^2+7x+12x-21)
We get rid of parentheses
-4x^2+7x+12x-21
We add all the numbers together, and all the variables
-4x^2+19x-21
Back to the equation:
-(-4x^2+19x-21)
-5x^2+4x^2+15x+3x-19x-9+21=0
We add all the numbers together, and all the variables
-1x^2-1x+12=0
a = -1; b = -1; c = +12;
Δ = b2-4ac
Δ = -12-4·(-1)·12
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*-1}=\frac{-6}{-2} =+3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*-1}=\frac{8}{-2} =-4 $
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