10w^2+51w+56=0

Solution for 10w^2+51w+56=0 equation:

10w^2+51w+56=0

a = 10; b = 51; c = +56;
Δ = b2-4ac
Δ = 512-4·10·56
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-19}{2*10}=\frac{-70}{20}
=-3+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+19}{2*10}=\frac{-32}{20}
=-1+3/5
$