(4x+6)(3-7x)=0

Solution for (4x+6)(3-7x)=0 equation:

(4x+6)(3-7x)=0

We add all the numbers together, and all the variables

(4x+6)(-7x+3)=0

We multiply parentheses ..

(-28x^2+12x-42x+18)=0

We get rid of parentheses

-28x^2+12x-42x+18=0

We add all the numbers together, and all the variables

-28x^2-30x+18=0

a = -28; b = -30; c = +18;
Δ = b2-4ac
Δ = -302-4·(-28)·18
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-54}{2*-28}=\frac{-24}{-56}
=3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+54}{2*-28}=\frac{84}{-56}
=-1+1/2
$