3(x+5)=2x(9x-10)

Solution for 3(x+5)=2x(9x-10) equation:

3(x+5)=2x(9x-10)

We move all terms to the left:

3(x+5)-(2x(9x-10))=0

We multiply parentheses

3x-(2x(9x-10))+15=0


We calculate terms in parentheses: -(2x(9x-10)), so:

2x(9x-10)

We multiply parentheses

18x^2-20x

Back to the equation:

-(18x^2-20x)


We get rid of parentheses

-18x^2+3x+20x+15=0

We add all the numbers together, and all the variables

-18x^2+23x+15=0

a = -18; b = 23; c = +15;
Δ = b2-4ac
Δ = 232-4·(-18)·15
Δ = 1609
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{-(23)-\sqrt{1609}}{2*-18}=\frac{-23-\sqrt{1609}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{1609}}{2*-18}=\frac{-23+\sqrt{1609}}{-36}
$