14w^2+41w=-15

Solution for 14w^2+41w=-15 equation:

14w^2+41w=-15

We move all terms to the left:

14w^2+41w-(-15)=0

We add all the numbers together, and all the variables

14w^2+41w+15=0

a = 14; b = 41; c = +15;
Δ = b2-4ac
Δ = 412-4·14·15
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-29}{2*14}=\frac{-70}{28}
=-2+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+29}{2*14}=\frac{-12}{28}
=-3/7
$