7=2x^2-3x-13

Solution for 7=2x^2-3x-13 equation:

7=2x^2-3x-13

We move all terms to the left:

7-(2x^2-3x-13)=0

We get rid of parentheses

-2x^2+3x+13+7=0

We add all the numbers together, and all the variables

-2x^2+3x+20=0

a = -2; b = 3; c = +20;
Δ = b2-4ac
Δ = 32-4·(-2)·20
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-13}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+13}{2*-2}=\frac{10}{-4}
=-2+1/2
$