-2x^2=2(11x-48)

Solution for -2x^2=2(11x-48) equation:

-2x^2=2(11x-48)

We move all terms to the left:

-2x^2-(2(11x-48))=0


We calculate terms in parentheses: -(2(11x-48)), so:

2(11x-48)

We multiply parentheses

22x-96

Back to the equation:

-(22x-96)


We get rid of parentheses

-2x^2-22x+96=0

a = -2; b = -22; c = +96;
Δ = b2-4ac
Δ = -222-4·(-2)·96
Δ = 1252
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:

$\sqrt{\Delta}=\sqrt{1252}=\sqrt{4*313}=\sqrt{4}*\sqrt{313}=2\sqrt{313}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{313}}{2*-2}=\frac{22-2\sqrt{313}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{313}}{2*-2}=\frac{22+2\sqrt{313}}{-4}
$