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

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

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

We multiply parentheses ..

(+42x^2-21x+24x-12)=0

We get rid of parentheses

42x^2-21x+24x-12=0

We add all the numbers together, and all the variables

42x^2+3x-12=0

a = 42; b = 3; c = -12;
Δ = b2-4ac
Δ = 32-4·42·(-12)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-45}{2*42}=\frac{-48}{84}
=-4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+45}{2*42}=\frac{42}{84}
=1/2
$