10-9x2+4x=-6x2

Solution for 10-9x2+4x=-6x2 equation:

10-9x^2+4x=-6x^2

We move all terms to the left:

10-9x^2+4x-(-6x^2)=0

We get rid of parentheses

-9x^2+6x^2+4x+10=0

We add all the numbers together, and all the variables

-3x^2+4x+10=0

a = -3; b = 4; c = +10;
Δ = b2-4ac
Δ = 42-4·(-3)·10
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{34}}{2*-3}=\frac{-4-2\sqrt{34}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{34}}{2*-3}=\frac{-4+2\sqrt{34}}{-6}
$