q^2+5q-34.59=0

Solution for q^2+5q-34.59=0 equation:

q^2+5q-34.59=0

a = 1; b = 5; c = -34.59;
Δ = b2-4ac
Δ = 52-4·1·(-34.59)
Δ = 163.36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{163.36}}{2*1}=\frac{-5-\sqrt{163.36}}{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{163.36}}{2*1}=\frac{-5+\sqrt{163.36}}{2}
$