28=4x(x+2)-13

Solution for 28=4x(x+2)-13 equation:

28=4x(x+2)-13

We move all terms to the left:

28-(4x(x+2)-13)=0


We calculate terms in parentheses: -(4x(x+2)-13), so:

4x(x+2)-13

We multiply parentheses

4x^2+8x-13

Back to the equation:

-(4x^2+8x-13)


We get rid of parentheses

-4x^2-8x+13+28=0

We add all the numbers together, and all the variables

-4x^2-8x+41=0

a = -4; b = -8; c = +41;
Δ = b2-4ac
Δ = -82-4·(-4)·41
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12\sqrt{5}}{2*-4}=\frac{8-12\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12\sqrt{5}}{2*-4}=\frac{8+12\sqrt{5}}{-8}
$