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

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

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

We multiply parentheses ..

(+12x^2+16x+18x+24)=0

We get rid of parentheses

12x^2+16x+18x+24=0

We add all the numbers together, and all the variables

12x^2+34x+24=0

a = 12; b = 34; c = +24;
Δ = b2-4ac
Δ = 342-4·12·24
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2}{2*12}=\frac{-36}{24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2}{2*12}=\frac{-32}{24}
=-1+1/3
$