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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-7x-12=0

a = 3; b = -7; c = -12;
Δ = b2-4ac
Δ = -72-4·3·(-12)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{193}}{2*3}=\frac{7-\sqrt{193}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{193}}{2*3}=\frac{7+\sqrt{193}}{6}
$