9x^2+30x=35+4x^2

Solution for 9x^2+30x=35+4x^2 equation:

9x^2+30x=35+4x^2

We move all terms to the left:

9x^2+30x-(35+4x^2)=0

We get rid of parentheses

9x^2-4x^2+30x-35=0

We add all the numbers together, and all the variables

5x^2+30x-35=0

a = 5; b = 30; c = -35;
Δ = b2-4ac
Δ = 302-4·5·(-35)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-40}{2*5}=\frac{-70}{10}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+40}{2*5}=\frac{10}{10}
=1
$