3x(2x+7)=105-x

Solution for 3x(2x+7)=105-x equation:

3x(2x+7)=105-x

We move all terms to the left:

3x(2x+7)-(105-x)=0

We add all the numbers together, and all the variables

3x(2x+7)-(-1x+105)=0

We multiply parentheses

6x^2+21x-(-1x+105)=0

We get rid of parentheses

6x^2+21x+1x-105=0

We add all the numbers together, and all the variables

6x^2+22x-105=0

a = 6; b = 22; c = -105;
Δ = b2-4ac
Δ = 222-4·6·(-105)
Δ = 3004
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:

$\sqrt{\Delta}=\sqrt{3004}=\sqrt{4*751}=\sqrt{4}*\sqrt{751}=2\sqrt{751}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{751}}{2*6}=\frac{-22-2\sqrt{751}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{751}}{2*6}=\frac{-22+2\sqrt{751}}{12}
$