4x(x+7)=49

Solution for 4x(x+7)=49 equation:

4x(x+7)=49

We move all terms to the left:

4x(x+7)-(49)=0

We multiply parentheses

4x^2+28x-49=0

a = 4; b = 28; c = -49;
Δ = b2-4ac
Δ = 282-4·4·(-49)
Δ = 1568
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:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28\sqrt{2}}{2*4}=\frac{-28-28\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28\sqrt{2}}{2*4}=\frac{-28+28\sqrt{2}}{8}
$