(12x^2+5x-7)/(4x+3)=0

Solution for (12x^2+5x-7)/(4x+3)=0 equation:

(12x^2+5x-7)/(4x+3)=0


Domain of the equation: (4x+3)!=0

We move all terms containing x to the left, all other terms to the right

4x!=-3

x!=-3/4

x!=-3/4

x∈R


We multiply all the terms by the denominator


(12x^2+5x-7)=0

We get rid of parentheses

12x^2+5x-7=0

a = 12; b = 5; c = -7;
Δ = b2-4ac
Δ = 52-4·12·(-7)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*12}=\frac{-24}{24}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*12}=\frac{14}{24}
=7/12
$