3x(3x+15)-(10+x)=35

Solution for 3x(3x+15)-(10+x)=35 equation:

3x(3x+15)-(10+x)=35

We move all terms to the left:

3x(3x+15)-(10+x)-(35)=0

We add all the numbers together, and all the variables

3x(3x+15)-(x+10)-35=0

We multiply parentheses

9x^2+45x-(x+10)-35=0

We get rid of parentheses

9x^2+45x-x-10-35=0

We add all the numbers together, and all the variables

9x^2+44x-45=0

a = 9; b = 44; c = -45;
Δ = b2-4ac
Δ = 442-4·9·(-45)
Δ = 3556
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:

$\sqrt{\Delta}=\sqrt{3556}=\sqrt{4*889}=\sqrt{4}*\sqrt{889}=2\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-2\sqrt{889}}{2*9}=\frac{-44-2\sqrt{889}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+2\sqrt{889}}{2*9}=\frac{-44+2\sqrt{889}}{18}
$