6+5x^2=15x-4x^2

Solution for 6+5x^2=15x-4x^2 equation:

6+5x^2=15x-4x^2

We move all terms to the left:

6+5x^2-(15x-4x^2)=0

We get rid of parentheses

5x^2+4x^2-15x+6=0

We add all the numbers together, and all the variables

9x^2-15x+6=0

a = 9; b = -15; c = +6;
Δ = b2-4ac
Δ = -152-4·9·6
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3}{2*9}=\frac{12}{18}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3}{2*9}=\frac{18}{18}
=1
$