8m2+3=13

Solution for 8m2+3=13 equation:

8m^2+3=13

We move all terms to the left:

8m^2+3-(13)=0

We add all the numbers together, and all the variables

8m^2-10=0

a = 8; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·8·(-10)
Δ = 320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*8}=\frac{0-8\sqrt{5}}{16}
=-\frac{8\sqrt{5}}{16}
=-\frac{\sqrt{5}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*8}=\frac{0+8\sqrt{5}}{16}
=\frac{8\sqrt{5}}{16}
=\frac{\sqrt{5}}{2}
$