10x(x+3)-(9x-4)=x-5+3

Solution for 10x(x+3)-(9x-4)=x-5+3 equation:

10x(x+3)-(9x-4)=x-5+3

We move all terms to the left:

10x(x+3)-(9x-4)-(x-5+3)=0

We add all the numbers together, and all the variables

10x(x+3)-(9x-4)-(x-2)=0

We multiply parentheses

10x^2+30x-(9x-4)-(x-2)=0

We get rid of parentheses

10x^2+30x-9x-x+4+2=0

We add all the numbers together, and all the variables

10x^2+20x+6=0

a = 10; b = 20; c = +6;
Δ = b2-4ac
Δ = 202-4·10·6
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{10}}{2*10}=\frac{-20-4\sqrt{10}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{10}}{2*10}=\frac{-20+4\sqrt{10}}{20}
$