x=(6x^2-4x-15x-10)-(3x^2-15x-9)

Solution for x=(6x^2-4x-15x-10)-(3x^2-15x-9) equation:

x=(6x^2-4x-15x-10)-(3x^2-15x-9)

We move all terms to the left:

x-((6x^2-4x-15x-10)-(3x^2-15x-9))=0


We calculate terms in parentheses: -((6x^2-4x-15x-10)-(3x^2-15x-9)), so:

(6x^2-4x-15x-10)-(3x^2-15x-9)

We get rid of parentheses

6x^2-3x^2-4x-15x+15x-10+9

We add all the numbers together, and all the variables

3x^2-4x-1

Back to the equation:

-(3x^2-4x-1)


We get rid of parentheses

-3x^2+x+4x+1=0

We add all the numbers together, and all the variables

-3x^2+5x+1=0

a = -3; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·(-3)·1
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{37}}{2*-3}=\frac{-5-\sqrt{37}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*-3}=\frac{-5+\sqrt{37}}{-6}
$