175=4m^2+24m+35

Solution for 175=4m^2+24m+35 equation:

175=4m^2+24m+35

We move all terms to the left:

175-(4m^2+24m+35)=0

We get rid of parentheses

-4m^2-24m-35+175=0

We add all the numbers together, and all the variables

-4m^2-24m+140=0

a = -4; b = -24; c = +140;
Δ = b2-4ac
Δ = -242-4·(-4)·140
Δ = 2816
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:

$\sqrt{\Delta}=\sqrt{2816}=\sqrt{256*11}=\sqrt{256}*\sqrt{11}=16\sqrt{11}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{11}}{2*-4}=\frac{24-16\sqrt{11}}{-8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{11}}{2*-4}=\frac{24+16\sqrt{11}}{-8}
$