3m^2-10m+1=-7

Solution for 3m^2-10m+1=-7 equation:

3m^2-10m+1=-7

We move all terms to the left:

3m^2-10m+1-(-7)=0

We add all the numbers together, and all the variables

3m^2-10m+8=0

a = 3; b = -10; c = +8;
Δ = b2-4ac
Δ = -102-4·3·8
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*3}=\frac{8}{6}
=1+1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*3}=\frac{12}{6}
=2
$