5m(2m-3)=35

Solution for 5m(2m-3)=35 equation:

5m(2m-3)=35

We move all terms to the left:

5m(2m-3)-(35)=0

We multiply parentheses

10m^2-15m-35=0

a = 10; b = -15; c = -35;
Δ = b2-4ac
Δ = -152-4·10·(-35)
Δ = 1625
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:

$\sqrt{\Delta}=\sqrt{1625}=\sqrt{25*65}=\sqrt{25}*\sqrt{65}=5\sqrt{65}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{65}}{2*10}=\frac{15-5\sqrt{65}}{20}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{65}}{2*10}=\frac{15+5\sqrt{65}}{20}
$