7(m-4)(m+1)=-34

Solution for 7(m-4)(m+1)=-34 equation:

7(m-4)(m+1)=-34

We move all terms to the left:

7(m-4)(m+1)-(-34)=0

We add all the numbers together, and all the variables

7(m-4)(m+1)+34=0

We multiply parentheses ..

7(+m^2+m-4m-4)+34=0

We multiply parentheses

7m^2+7m-28m-28+34=0

We add all the numbers together, and all the variables

7m^2-21m+6=0

a = 7; b = -21; c = +6;
Δ = b2-4ac
Δ = -212-4·7·6
Δ = 273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{273}}{2*7}=\frac{21-\sqrt{273}}{14}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{273}}{2*7}=\frac{21+\sqrt{273}}{14}
$