4w*w=13

Solution for 4w*w=13 equation:

4w*w=13

We move all terms to the left:

4w*w-(13)=0

Wy multiply elements

4w^2-13=0

a = 4; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·4·(-13)
Δ = 208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{13}}{2*4}=\frac{0-4\sqrt{13}}{8}
=-\frac{4\sqrt{13}}{8}
=-\frac{\sqrt{13}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{13}}{2*4}=\frac{0+4\sqrt{13}}{8}
=\frac{4\sqrt{13}}{8}
=\frac{\sqrt{13}}{2}
$