0.2x^2+14x=480+10x

Solution for 0.2x^2+14x=480+10x equation:

0.2x^2+14x=480+10x

We move all terms to the left:

0.2x^2+14x-(480+10x)=0

We add all the numbers together, and all the variables

0.2x^2+14x-(10x+480)=0

We get rid of parentheses

0.2x^2+14x-10x-480=0

We add all the numbers together, and all the variables

0.2x^2+4x-480=0

a = 0.2; b = 4; c = -480;
Δ = b2-4ac
Δ = 42-4·0.2·(-480)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-20}{2*0.2}=\frac{-24}{0.4}
=-60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20}{2*0.2}=\frac{16}{0.4}
=40
$