5x^2=200-15x

Solution for 5x^2=200-15x equation:

5x^2=200-15x

We move all terms to the left:

5x^2-(200-15x)=0

We add all the numbers together, and all the variables

5x^2-(-15x+200)=0

We get rid of parentheses

5x^2+15x-200=0

a = 5; b = 15; c = -200;
Δ = b2-4ac
Δ = 152-4·5·(-200)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-65}{2*5}=\frac{-80}{10}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+65}{2*5}=\frac{50}{10}
=5
$