4x^2-52x=-48

Solution for 4x^2-52x=-48 equation:

4x^2-52x=-48

We move all terms to the left:

4x^2-52x-(-48)=0

We add all the numbers together, and all the variables

4x^2-52x+48=0

a = 4; b = -52; c = +48;
Δ = b2-4ac
Δ = -522-4·4·48
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-44}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+44}{2*4}=\frac{96}{8}
=12
$