5x^2=360(6.5-x)

Solution for 5x^2=360(6.5-x) equation:

5x^2=360(6.5-x)

We move all terms to the left:

5x^2-(360(6.5-x))=0

We add all the numbers together, and all the variables

5x^2-(360(-1x+6.5))=0


We calculate terms in parentheses: -(360(-1x+6.5)), so:

360(-1x+6.5)

We multiply parentheses

-360x+2340

Back to the equation:

-(-360x+2340)


We get rid of parentheses

5x^2+360x-2340=0

a = 5; b = 360; c = -2340;
Δ = b2-4ac
Δ = 3602-4·5·(-2340)
Δ = 176400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{176400}=420$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-420}{2*5}=\frac{-780}{10}
=-78
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+420}{2*5}=\frac{60}{10}
=6
$