(m-12)(8m-2)=10

Solution for (m-12)(8m-2)=10 equation:

(m-12)(8m-2)=10

We move all terms to the left:

(m-12)(8m-2)-(10)=0

We multiply parentheses ..

(+8m^2-2m-96m+24)-10=0

We get rid of parentheses

8m^2-2m-96m+24-10=0

We add all the numbers together, and all the variables

8m^2-98m+14=0

a = 8; b = -98; c = +14;
Δ = b2-4ac
Δ = -982-4·8·14
Δ = 9156
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:

$\sqrt{\Delta}=\sqrt{9156}=\sqrt{4*2289}=\sqrt{4}*\sqrt{2289}=2\sqrt{2289}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-2\sqrt{2289}}{2*8}=\frac{98-2\sqrt{2289}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+2\sqrt{2289}}{2*8}=\frac{98+2\sqrt{2289}}{16}
$