5x(x+3)=13(9x+18)-5

Solution for 5x(x+3)=13(9x+18)-5 equation:

5x(x+3)=13(9x+18)-5

We move all terms to the left:

5x(x+3)-(13(9x+18)-5)=0

We multiply parentheses

5x^2+15x-(13(9x+18)-5)=0


We calculate terms in parentheses: -(13(9x+18)-5), so:

13(9x+18)-5

We multiply parentheses

117x+234-5

We add all the numbers together, and all the variables

117x+229

Back to the equation:

-(117x+229)


We get rid of parentheses

5x^2+15x-117x-229=0

We add all the numbers together, and all the variables

5x^2-102x-229=0

a = 5; b = -102; c = -229;
Δ = b2-4ac
Δ = -1022-4·5·(-229)
Δ = 14984
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:

$\sqrt{\Delta}=\sqrt{14984}=\sqrt{4*3746}=\sqrt{4}*\sqrt{3746}=2\sqrt{3746}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-2\sqrt{3746}}{2*5}=\frac{102-2\sqrt{3746}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+2\sqrt{3746}}{2*5}=\frac{102+2\sqrt{3746}}{10}
$