4x^2-94x=-49

Solution for 4x^2-94x=-49 equation:

4x^2-94x=-49

We move all terms to the left:

4x^2-94x-(-49)=0

We add all the numbers together, and all the variables

4x^2-94x+49=0

a = 4; b = -94; c = +49;
Δ = b2-4ac
Δ = -942-4·4·49
Δ = 8052
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:

$\sqrt{\Delta}=\sqrt{8052}=\sqrt{4*2013}=\sqrt{4}*\sqrt{2013}=2\sqrt{2013}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-94)-2\sqrt{2013}}{2*4}=\frac{94-2\sqrt{2013}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-94)+2\sqrt{2013}}{2*4}=\frac{94+2\sqrt{2013}}{8}
$