2(x^2-14x-240)=0

Solution for 2(x^2-14x-240)=0 equation:

2(x^2-14x-240)=0

We multiply parentheses

2x^2-28x-480=0

a = 2; b = -28; c = -480;
Δ = b2-4ac
Δ = -282-4·2·(-480)
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-68}{2*2}=\frac{-40}{4}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+68}{2*2}=\frac{96}{4}
=24
$