(x+4)(x+7)=776x

Solution for (x+4)(x+7)=776x equation:

(x+4)(x+7)=776x

We move all terms to the left:

(x+4)(x+7)-(776x)=0

We add all the numbers together, and all the variables

-776x+(x+4)(x+7)=0

We multiply parentheses ..

(+x^2+7x+4x+28)-776x=0

We get rid of parentheses

x^2+7x+4x-776x+28=0

We add all the numbers together, and all the variables

x^2-765x+28=0

a = 1; b = -765; c = +28;
Δ = b2-4ac
Δ = -7652-4·1·28
Δ = 585113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-765)-\sqrt{585113}}{2*1}=\frac{765-\sqrt{585113}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-765)+\sqrt{585113}}{2*1}=\frac{765+\sqrt{585113}}{2}
$