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(12x+9)(2-7x)-(12x+9)=0
We add all the numbers together, and all the variables
(12x+9)(-7x+2)-(12x+9)=0
We get rid of parentheses
(12x+9)(-7x+2)-12x-9=0
We multiply parentheses ..
(-84x^2+24x-63x+18)-12x-9=0
We get rid of parentheses
-84x^2+24x-63x-12x+18-9=0
We add all the numbers together, and all the variables
-84x^2-51x+9=0
a = -84; b = -51; c = +9;
Δ = b2-4ac
Δ = -512-4·(-84)·9
Δ = 5625
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{5625}=75$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-75}{2*-84}=\frac{-24}{-168} =1/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+75}{2*-84}=\frac{126}{-168} =-3/4 $
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