7x-2x^2=-13

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

7x-2x^2=-13

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

a = -2; b = 7; c = +13;
Δ = b2-4ac
Δ = 72-4·(-2)·13
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{17}}{2*-2}=\frac{-7-3\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{17}}{2*-2}=\frac{-7+3\sqrt{17}}{-4}
$