5x^2=30-65x

Solution for 5x^2=30-65x equation:

5x^2=30-65x

We move all terms to the left:

5x^2-(30-65x)=0

We add all the numbers together, and all the variables

5x^2-(-65x+30)=0

We get rid of parentheses

5x^2+65x-30=0

a = 5; b = 65; c = -30;
Δ = b2-4ac
Δ = 652-4·5·(-30)
Δ = 4825
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:

$\sqrt{\Delta}=\sqrt{4825}=\sqrt{25*193}=\sqrt{25}*\sqrt{193}=5\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-5\sqrt{193}}{2*5}=\frac{-65-5\sqrt{193}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+5\sqrt{193}}{2*5}=\frac{-65+5\sqrt{193}}{10}
$