8x^2=13-4x

Solution for 8x^2=13-4x equation:

8x^2=13-4x

We move all terms to the left:

8x^2-(13-4x)=0

We add all the numbers together, and all the variables

8x^2-(-4x+13)=0

We get rid of parentheses

8x^2+4x-13=0

a = 8; b = 4; c = -13;
Δ = b2-4ac
Δ = 42-4·8·(-13)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12\sqrt{3}}{2*8}=\frac{-4-12\sqrt{3}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12\sqrt{3}}{2*8}=\frac{-4+12\sqrt{3}}{16}
$