8m2+16m=43

Solution for 8m2+16m=43 equation:

8m^2+16m=43

We move all terms to the left:

8m^2+16m-(43)=0

a = 8; b = 16; c = -43;
Δ = b2-4ac
Δ = 162-4·8·(-43)
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{102}}{2*8}=\frac{-16-4\sqrt{102}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{102}}{2*8}=\frac{-16+4\sqrt{102}}{16}
$