-10x^2+6x-59=-4-11x^2

Solution for -10x^2+6x-59=-4-11x^2 equation:

-10x^2+6x-59=-4-11x^2

We move all terms to the left:

-10x^2+6x-59-(-4-11x^2)=0

We get rid of parentheses

-10x^2+11x^2+6x+4-59=0

We add all the numbers together, and all the variables

x^2+6x-55=0

a = 1; b = 6; c = -55;
Δ = b2-4ac
Δ = 62-4·1·(-55)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-16}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+16}{2*1}=\frac{10}{2}
=5
$