11-15x-7x^2=25-16x^2

Solution for 11-15x-7x^2=25-16x^2 equation:

11-15x-7x^2=25-16x^2

We move all terms to the left:

11-15x-7x^2-(25-16x^2)=0

We get rid of parentheses

-7x^2+16x^2-15x-25+11=0

We add all the numbers together, and all the variables

9x^2-15x-14=0

a = 9; b = -15; c = -14;
Δ = b2-4ac
Δ = -152-4·9·(-14)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-27}{2*9}=\frac{-12}{18}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+27}{2*9}=\frac{42}{18}
=2+1/3
$