2x^2+10x-48=1080

Solution for 2x^2+10x-48=1080 equation:

2x^2+10x-48=1080

We move all terms to the left:

2x^2+10x-48-(1080)=0

We add all the numbers together, and all the variables

2x^2+10x-1128=0

a = 2; b = 10; c = -1128;
Δ = b2-4ac
Δ = 102-4·2·(-1128)
Δ = 9124
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:

$\sqrt{\Delta}=\sqrt{9124}=\sqrt{4*2281}=\sqrt{4}*\sqrt{2281}=2\sqrt{2281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{2281}}{2*2}=\frac{-10-2\sqrt{2281}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{2281}}{2*2}=\frac{-10+2\sqrt{2281}}{4}
$