7x(-3x+7)-4(-3x+7)=0

Solution for 7x(-3x+7)-4(-3x+7)=0 equation:

7x(-3x+7)-4(-3x+7)=0

We multiply parentheses

-21x^2+49x+12x-28=0

We add all the numbers together, and all the variables

-21x^2+61x-28=0

a = -21; b = 61; c = -28;
Δ = b2-4ac
Δ = 612-4·(-21)·(-28)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-37}{2*-21}=\frac{-98}{-42}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+37}{2*-21}=\frac{-24}{-42}
=4/7
$