10m2=7m+17

Solution for 10m2=7m+17 equation:

10m^2=7m+17

We move all terms to the left:

10m^2-(7m+17)=0

We get rid of parentheses

10m^2-7m-17=0

a = 10; b = -7; c = -17;
Δ = b2-4ac
Δ = -72-4·10·(-17)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-27}{2*10}=\frac{-20}{20}
=-1
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+27}{2*10}=\frac{34}{20}
=1+7/10
$