(x*x)+4x=13

Solution for (x*x)+4x=13 equation:

(x*x)+4x=13

We move all terms to the left:

(x*x)+4x-(13)=0

We add all the numbers together, and all the variables

(+x*x)+4x-13=0

We add all the numbers together, and all the variables

4x+(+x*x)-13=0

We get rid of parentheses

4x+x*x-13=0

Wy multiply elements

x^2+4x-13=0

a = 1; b = 4; c = -13;
Δ = b2-4ac
Δ = 42-4·1·(-13)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{17}}{2*1}=\frac{-4-2\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{17}}{2*1}=\frac{-4+2\sqrt{17}}{2}
$