2.5x^2+10-240=0

Solution for 2.5x^2+10-240=0 equation:

2.5x^2+10-240=0

We add all the numbers together, and all the variables

2.5x^2-230=0

a = 2.5; b = 0; c = -230;
Δ = b2-4ac
Δ = 02-4·2.5·(-230)
Δ = 2300
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:

$\sqrt{\Delta}=\sqrt{2300}=\sqrt{100*23}=\sqrt{100}*\sqrt{23}=10\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{23}}{2*2.5}=\frac{0-10\sqrt{23}}{5}
=-\frac{10\sqrt{23}}{5}
=-2\sqrt{23}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{23}}{2*2.5}=\frac{0+10\sqrt{23}}{5}
=\frac{10\sqrt{23}}{5}
=2\sqrt{23}
$