4(v^2-11v+18)=0

Solution for 4(v^2-11v+18)=0 equation:

4(v^2-11v+18)=0

We multiply parentheses

4v^2-44v+72=0

a = 4; b = -44; c = +72;
Δ = b2-4ac
Δ = -442-4·4·72
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-28}{2*4}=\frac{16}{8}
=2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+28}{2*4}=\frac{72}{8}
=9
$