4x(7+x)=10

Solution for 4x(7+x)=10 equation:

4x(7+x)=10

We move all terms to the left:

4x(7+x)-(10)=0

We add all the numbers together, and all the variables

4x(x+7)-10=0

We multiply parentheses

4x^2+28x-10=0

a = 4; b = 28; c = -10;
Δ = b2-4ac
Δ = 282-4·4·(-10)
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{59}}{2*4}=\frac{-28-4\sqrt{59}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{59}}{2*4}=\frac{-28+4\sqrt{59}}{8}
$