2w^2-14w=-12

Solution for 2w^2-14w=-12 equation:

2w^2-14w=-12

We move all terms to the left:

2w^2-14w-(-12)=0

We add all the numbers together, and all the variables

2w^2-14w+12=0

a = 2; b = -14; c = +12;
Δ = b2-4ac
Δ = -142-4·2·12
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10}{2*2}=\frac{4}{4}
=1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*2}=\frac{24}{4}
=6
$