111=(8x+14)(7x+5)

Solution for 111=(8x+14)(7x+5) equation:

111=(8x+14)(7x+5)

We move all terms to the left:

111-((8x+14)(7x+5))=0

We multiply parentheses ..

-((+56x^2+40x+98x+70))+111=0


We calculate terms in parentheses: -((+56x^2+40x+98x+70)), so:

(+56x^2+40x+98x+70)

We get rid of parentheses

56x^2+40x+98x+70

We add all the numbers together, and all the variables

56x^2+138x+70

Back to the equation:

-(56x^2+138x+70)


We get rid of parentheses

-56x^2-138x-70+111=0

We add all the numbers together, and all the variables

-56x^2-138x+41=0

a = -56; b = -138; c = +41;
Δ = b2-4ac
Δ = -1382-4·(-56)·41
Δ = 28228
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28228}=\sqrt{4*7057}=\sqrt{4}*\sqrt{7057}=2\sqrt{7057}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-2\sqrt{7057}}{2*-56}=\frac{138-2\sqrt{7057}}{-112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+2\sqrt{7057}}{2*-56}=\frac{138+2\sqrt{7057}}{-112}
$