4x^2+48x-147=7

Solution for 4x^2+48x-147=7 equation:

4x^2+48x-147=7

We move all terms to the left:

4x^2+48x-147-(7)=0

We add all the numbers together, and all the variables

4x^2+48x-154=0

a = 4; b = 48; c = -154;
Δ = b2-4ac
Δ = 482-4·4·(-154)
Δ = 4768
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:

$\sqrt{\Delta}=\sqrt{4768}=\sqrt{16*298}=\sqrt{16}*\sqrt{298}=4\sqrt{298}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{298}}{2*4}=\frac{-48-4\sqrt{298}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{298}}{2*4}=\frac{-48+4\sqrt{298}}{8}
$