-2.4x^2+278.4x-6342=588

Solution for -2.4x^2+278.4x-6342=588 equation:

-2.4x^2+278.4x-6342=588

We move all terms to the left:

-2.4x^2+278.4x-6342-(588)=0

We add all the numbers together, and all the variables

-2.4x^2+278.4x-6930=0

a = -2.4; b = 278.4; c = -6930;
Δ = b2-4ac
Δ = 278.42-4·(-2.4)·(-6930)
Δ = 10978.56
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(278.4)-\sqrt{10978.56}}{2*-2.4}=\frac{-278.4-\sqrt{10978.56}}{-4.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(278.4)+\sqrt{10978.56}}{2*-2.4}=\frac{-278.4+\sqrt{10978.56}}{-4.8}
$