(3x+8)-(2x+7)x=3

Solution for (3x+8)-(2x+7)x=3 equation:

(3x+8)-(2x+7)x=3

We move all terms to the left:

(3x+8)-(2x+7)x-(3)=0

We multiply parentheses

-2x^2+(3x+8)-7x-3=0

We get rid of parentheses

-2x^2+3x-7x+8-3=0

We add all the numbers together, and all the variables

-2x^2-4x+5=0

a = -2; b = -4; c = +5;
Δ = b2-4ac
Δ = -42-4·(-2)·5
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{14}}{2*-2}=\frac{4-2\sqrt{14}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{14}}{2*-2}=\frac{4+2\sqrt{14}}{-4}
$