2m^2-3=175

Solution for 2m^2-3=175 equation:

2m^2-3=175

We move all terms to the left:

2m^2-3-(175)=0

We add all the numbers together, and all the variables

2m^2-178=0

a = 2; b = 0; c = -178;
Δ = b2-4ac
Δ = 02-4·2·(-178)
Δ = 1424
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:

$\sqrt{\Delta}=\sqrt{1424}=\sqrt{16*89}=\sqrt{16}*\sqrt{89}=4\sqrt{89}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{89}}{2*2}=\frac{0-4\sqrt{89}}{4}
=-\frac{4\sqrt{89}}{4}
=-\sqrt{89}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{89}}{2*2}=\frac{0+4\sqrt{89}}{4}
=\frac{4\sqrt{89}}{4}
=\sqrt{89}
$