(6-7x)(3x-2)=-1

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Solution for (6-7x)(3x-2)=-1 equation:



(6-7x)(3x-2)=-1
We move all terms to the left:
(6-7x)(3x-2)-(-1)=0
We add all the numbers together, and all the variables
(-7x+6)(3x-2)-(-1)=0
We add all the numbers together, and all the variables
(-7x+6)(3x-2)+1=0
We multiply parentheses ..
(-21x^2+14x+18x-12)+1=0
We get rid of parentheses
-21x^2+14x+18x-12+1=0
We add all the numbers together, and all the variables
-21x^2+32x-11=0
a = -21; b = 32; c = -11;
Δ = b2-4ac
Δ = 322-4·(-21)·(-11)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-10}{2*-21}=\frac{-42}{-42} =1 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+10}{2*-21}=\frac{-22}{-42} =11/21 $

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