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(3-x)(x-4)-(2x-3)(x-4)+(x+7)(x-2)=31
We move all terms to the left:
(3-x)(x-4)-(2x-3)(x-4)+(x+7)(x-2)-(31)=0
We add all the numbers together, and all the variables
(-1x+3)(x-4)-(2x-3)(x-4)+(x+7)(x-2)-31=0
We multiply parentheses ..
(-1x^2+4x+3x-12)-(2x-3)(x-4)+(x+7)(x-2)-31=0
We get rid of parentheses
-1x^2+4x+3x-(2x-3)(x-4)+(x+7)(x-2)-12-31=0
We multiply parentheses ..
-1x^2-(+2x^2-8x-3x+12)+4x+3x+(x+7)(x-2)-12-31=0
We add all the numbers together, and all the variables
-1x^2-(+2x^2-8x-3x+12)+7x+(x+7)(x-2)-43=0
We get rid of parentheses
-1x^2-2x^2+8x+3x+7x+(x+7)(x-2)-12-43=0
We multiply parentheses ..
-1x^2-2x^2+(+x^2-2x+7x-14)+8x+3x+7x-12-43=0
We add all the numbers together, and all the variables
-3x^2+(+x^2-2x+7x-14)+18x-55=0
We get rid of parentheses
-3x^2+x^2-2x+7x+18x-14-55=0
We add all the numbers together, and all the variables
-2x^2+23x-69=0
a = -2; b = 23; c = -69;
Δ = b2-4ac
Δ = 232-4·(-2)·(-69)
Δ = -23
Delta is less than zero, so there is no solution for the equation
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