26m^2+24=5m^2-171m

Solution for 26m^2+24=5m^2-171m equation:

26m^2+24=5m^2-171m

We move all terms to the left:

26m^2+24-(5m^2-171m)=0

We get rid of parentheses

26m^2-5m^2+171m+24=0

We add all the numbers together, and all the variables

21m^2+171m+24=0

a = 21; b = 171; c = +24;
Δ = b2-4ac
Δ = 1712-4·21·24
Δ = 27225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{27225}=165$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(171)-165}{2*21}=\frac{-336}{42}
=-8
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(171)+165}{2*21}=\frac{-6}{42}
=-1/7
$