30x^2+25x-55=6x^2-11x-10

Solution for 30x^2+25x-55=6x^2-11x-10 equation:

30x^2+25x-55=6x^2-11x-10

We move all terms to the left:

30x^2+25x-55-(6x^2-11x-10)=0

We get rid of parentheses

30x^2-6x^2+25x+11x+10-55=0

We add all the numbers together, and all the variables

24x^2+36x-45=0

a = 24; b = 36; c = -45;
Δ = b2-4ac
Δ = 362-4·24·(-45)
Δ = 5616
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:

$\sqrt{\Delta}=\sqrt{5616}=\sqrt{144*39}=\sqrt{144}*\sqrt{39}=12\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{39}}{2*24}=\frac{-36-12\sqrt{39}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{39}}{2*24}=\frac{-36+12\sqrt{39}}{48}
$