5(3x+9)2x=15x-2(x-5)

Solution for 5(3x+9)2x=15x-2(x-5) equation:

5(3x+9)2x=15x-2(x-5)

We move all terms to the left:

5(3x+9)2x-(15x-2(x-5))=0

We multiply parentheses

30x^2+90x-(15x-2(x-5))=0


We calculate terms in parentheses: -(15x-2(x-5)), so:

15x-2(x-5)

We multiply parentheses

15x-2x+10

We add all the numbers together, and all the variables

13x+10

Back to the equation:

-(13x+10)


We get rid of parentheses

30x^2+90x-13x-10=0

We add all the numbers together, and all the variables

30x^2+77x-10=0

a = 30; b = 77; c = -10;
Δ = b2-4ac
Δ = 772-4·30·(-10)
Δ = 7129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-\sqrt{7129}}{2*30}=\frac{-77-\sqrt{7129}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+\sqrt{7129}}{2*30}=\frac{-77+\sqrt{7129}}{60}
$