(4x+3)(-6x+1)=3

Solution for (4x+3)(-6x+1)=3 equation:

(4x+3)(-6x+1)=3

We move all terms to the left:

(4x+3)(-6x+1)-(3)=0

We multiply parentheses ..

(-24x^2+4x-18x+3)-3=0

We get rid of parentheses

-24x^2+4x-18x+3-3=0

We add all the numbers together, and all the variables

-24x^2-14x=0

a = -24; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-24)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-24}=\frac{28}{-48}
=-7/12
$