-7x(x+6)+50=14-8x

Solution for -7x(x+6)+50=14-8x equation:

-7x(x+6)+50=14-8x

We move all terms to the left:

-7x(x+6)+50-(14-8x)=0

We add all the numbers together, and all the variables

-7x(x+6)-(-8x+14)+50=0

We multiply parentheses

-7x^2-42x-(-8x+14)+50=0

We get rid of parentheses

-7x^2-42x+8x-14+50=0

We add all the numbers together, and all the variables

-7x^2-34x+36=0

a = -7; b = -34; c = +36;
Δ = b2-4ac
Δ = -342-4·(-7)·36
Δ = 2164
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:

$\sqrt{\Delta}=\sqrt{2164}=\sqrt{4*541}=\sqrt{4}*\sqrt{541}=2\sqrt{541}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{541}}{2*-7}=\frac{34-2\sqrt{541}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{541}}{2*-7}=\frac{34+2\sqrt{541}}{-14}
$