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(3x+7)(2x-9)-(3x+7)(5x-7)=0
We multiply parentheses ..
(+6x^2-27x+14x-63)-(3x+7)(5x-7)=0
We get rid of parentheses
6x^2-27x+14x-(3x+7)(5x-7)-63=0
We multiply parentheses ..
6x^2-(+15x^2-21x+35x-49)-27x+14x-63=0
We add all the numbers together, and all the variables
6x^2-(+15x^2-21x+35x-49)-13x-63=0
We get rid of parentheses
6x^2-15x^2+21x-35x-13x+49-63=0
We add all the numbers together, and all the variables
-9x^2-27x-14=0
a = -9; b = -27; c = -14;
Δ = b2-4ac
Δ = -272-4·(-9)·(-14)
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-15}{2*-9}=\frac{12}{-18} =-2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+15}{2*-9}=\frac{42}{-18} =-2+1/3 $
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