(2x+3)/12x2=1

Solution for (2x+3)/12x2=1 equation:

(2x+3)/12x^2=1

We move all terms to the left:

(2x+3)/12x^2-(1)=0


Domain of the equation: 12x^2!=0

x^2!=0/12

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


(2x+3)-1*12x^2=0

Wy multiply elements

-12x^2+(2x+3)=0

We get rid of parentheses

-12x^2+2x+3=0

a = -12; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-12)·3
Δ = 148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{37}}{2*-12}=\frac{-2-2\sqrt{37}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{37}}{2*-12}=\frac{-2+2\sqrt{37}}{-24}
$