6=2x^2+7x-13

Solution for 6=2x^2+7x-13 equation:

6=2x^2+7x-13

We move all terms to the left:

6-(2x^2+7x-13)=0

We get rid of parentheses

-2x^2-7x+13+6=0

We add all the numbers together, and all the variables

-2x^2-7x+19=0

a = -2; b = -7; c = +19;
Δ = b2-4ac
Δ = -72-4·(-2)·19
Δ = 201
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{-(-7)-\sqrt{201}}{2*-2}=\frac{7-\sqrt{201}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{201}}{2*-2}=\frac{7+\sqrt{201}}{-4}
$