5x^2+12x+8=48

Solution for 5x^2+12x+8=48 equation:

5x^2+12x+8=48

We move all terms to the left:

5x^2+12x+8-(48)=0

We add all the numbers together, and all the variables

5x^2+12x-40=0

a = 5; b = 12; c = -40;
Δ = b2-4ac
Δ = 122-4·5·(-40)
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{-(12)-4\sqrt{59}}{2*5}=\frac{-12-4\sqrt{59}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{59}}{2*5}=\frac{-12+4\sqrt{59}}{10}
$