190=(w+14)(w+10)

Solution for 190=(w+14)(w+10) equation:

190=(w+14)(w+10)

We move all terms to the left:

190-((w+14)(w+10))=0

We multiply parentheses ..

-((+w^2+10w+14w+140))+190=0


We calculate terms in parentheses: -((+w^2+10w+14w+140)), so:

(+w^2+10w+14w+140)

We get rid of parentheses

w^2+10w+14w+140

We add all the numbers together, and all the variables

w^2+24w+140

Back to the equation:

-(w^2+24w+140)


We get rid of parentheses

-w^2-24w-140+190=0

We add all the numbers together, and all the variables

-1w^2-24w+50=0

a = -1; b = -24; c = +50;
Δ = b2-4ac
Δ = -242-4·(-1)·50
Δ = 776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{194}}{2*-1}=\frac{24-2\sqrt{194}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{194}}{2*-1}=\frac{24+2\sqrt{194}}{-2}
$