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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-4x+4=0

a = -2; b = -4; c = +4;
Δ = b2-4ac
Δ = -42-4·(-2)·4
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{3}}{2*-2}=\frac{4-4\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{3}}{2*-2}=\frac{4+4\sqrt{3}}{-4}
$