6X(3x-7)-7(7-3x)=0

Solution for 6X(3x-7)-7(7-3x)=0 equation:

6X(3X-7)-7(7-3X)=0

We add all the numbers together, and all the variables

6X(3X-7)-7(-3X+7)=0

We multiply parentheses

18X^2-42X+21X-49=0

We add all the numbers together, and all the variables

18X^2-21X-49=0

a = 18; b = -21; c = -49;
Δ = b2-4ac
Δ = -212-4·18·(-49)
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-63}{2*18}=\frac{-42}{36}
=-1+1/6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+63}{2*18}=\frac{84}{36}
=2+1/3
$