7x-3=3(x+1)4x-6

Solution for 7x-3=3(x+1)4x-6 equation:

7x-3=3(x+1)4x-6

We move all terms to the left:

7x-3-(3(x+1)4x-6)=0


We calculate terms in parentheses: -(3(x+1)4x-6), so:

3(x+1)4x-6

We multiply parentheses

12x^2+12x-6

Back to the equation:

-(12x^2+12x-6)


We get rid of parentheses

-12x^2+7x-12x+6-3=0

We add all the numbers together, and all the variables

-12x^2-5x+3=0

a = -12; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·(-12)·3
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*-12}=\frac{-8}{-24}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*-12}=\frac{18}{-24}
=-3/4
$