144=2x^2-3x-1

Solution for 144=2x^2-3x-1 equation:

144=2x^2-3x-1

We move all terms to the left:

144-(2x^2-3x-1)=0

We get rid of parentheses

-2x^2+3x+1+144=0

We add all the numbers together, and all the variables

-2x^2+3x+145=0

a = -2; b = 3; c = +145;
Δ = b2-4ac
Δ = 32-4·(-2)·145
Δ = 1169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{1169}}{2*-2}=\frac{-3-\sqrt{1169}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{1169}}{2*-2}=\frac{-3+\sqrt{1169}}{-4}
$