10x-(x-19)=2x(2)+x

Solution for 10x-(x-19)=2x(2)+x equation:

10x-(x-19)=2x(2)+x

We move all terms to the left:

10x-(x-19)-(2x(2)+x)=0

We add all the numbers together, and all the variables

-(+2x^2+x)+10x-(x-19)=0

We get rid of parentheses

-2x^2-x+10x-x+19=0

We add all the numbers together, and all the variables

-2x^2+8x+19=0

a = -2; b = 8; c = +19;
Δ = b2-4ac
Δ = 82-4·(-2)·19
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{6}}{2*-2}=\frac{-8-6\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{6}}{2*-2}=\frac{-8+6\sqrt{6}}{-4}
$