5x+3=2x^2-3x-1

Solution for 5x+3=2x^2-3x-1 equation:

5x+3=2x^2-3x-1

We move all terms to the left:

5x+3-(2x^2-3x-1)=0

We get rid of parentheses

-2x^2+5x+3x+1+3=0

We add all the numbers together, and all the variables

-2x^2+8x+4=0

a = -2; b = 8; c = +4;
Δ = b2-4ac
Δ = 82-4·(-2)·4
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*-2}=\frac{-8-4\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*-2}=\frac{-8+4\sqrt{6}}{-4}
$