(3x+5)2-9x2=10x+5

Solution for (3x+5)2-9x2=10x+5 equation:

(3x+5)2-9x^2=10x+5

We move all terms to the left:

(3x+5)2-9x^2-(10x+5)=0

We multiply parentheses

-9x^2+6x-(10x+5)+10=0

We get rid of parentheses

-9x^2+6x-10x-5+10=0

We add all the numbers together, and all the variables

-9x^2-4x+5=0

a = -9; b = -4; c = +5;
Δ = b2-4ac
Δ = -42-4·(-9)·5
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-14}{2*-9}=\frac{-10}{-18}
=5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+14}{2*-9}=\frac{18}{-18}
=-1
$