(7x+6)(4x+9)=0

Solution for (7x+6)(4x+9)=0 equation:

(7x+6)(4x+9)=0

We multiply parentheses ..

(+28x^2+63x+24x+54)=0

We get rid of parentheses

28x^2+63x+24x+54=0

We add all the numbers together, and all the variables

28x^2+87x+54=0

a = 28; b = 87; c = +54;
Δ = b2-4ac
Δ = 872-4·28·54
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(87)-39}{2*28}=\frac{-126}{56}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+39}{2*28}=\frac{-48}{56}
=-6/7
$