10x^2=36-9x

Solution for 10x^2=36-9x equation:

10x^2=36-9x

We move all terms to the left:

10x^2-(36-9x)=0

We add all the numbers together, and all the variables

10x^2-(-9x+36)=0

We get rid of parentheses

10x^2+9x-36=0

a = 10; b = 9; c = -36;
Δ = b2-4ac
Δ = 92-4·10·(-36)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-39}{2*10}=\frac{-48}{20}
=-2+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+39}{2*10}=\frac{30}{20}
=1+1/2
$