6x(2x+3)=7(1-x)

Solution for 6x(2x+3)=7(1-x) equation:

6x(2x+3)=7(1-x)

We move all terms to the left:

6x(2x+3)-(7(1-x))=0

We add all the numbers together, and all the variables

6x(2x+3)-(7(-1x+1))=0

We multiply parentheses

12x^2+18x-(7(-1x+1))=0


We calculate terms in parentheses: -(7(-1x+1)), so:

7(-1x+1)

We multiply parentheses

-7x+7

Back to the equation:

-(-7x+7)


We get rid of parentheses

12x^2+18x+7x-7=0

We add all the numbers together, and all the variables

12x^2+25x-7=0

a = 12; b = 25; c = -7;
Δ = b2-4ac
Δ = 252-4·12·(-7)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-31}{2*12}=\frac{-56}{24}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+31}{2*12}=\frac{6}{24}
=1/4
$