5x(2x-3)=9x-(7x+2)

Solution for 5x(2x-3)=9x-(7x+2) equation:

5x(2x-3)=9x-(7x+2)

We move all terms to the left:

5x(2x-3)-(9x-(7x+2))=0

We multiply parentheses

10x^2-15x-(9x-(7x+2))=0


We calculate terms in parentheses: -(9x-(7x+2)), so:

9x-(7x+2)

We get rid of parentheses

9x-7x-2

We add all the numbers together, and all the variables

2x-2

Back to the equation:

-(2x-2)


We get rid of parentheses

10x^2-15x-2x+2=0

We add all the numbers together, and all the variables

10x^2-17x+2=0

a = 10; b = -17; c = +2;
Δ = b2-4ac
Δ = -172-4·10·2
Δ = 209
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{-(-17)-\sqrt{209}}{2*10}=\frac{17-\sqrt{209}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{209}}{2*10}=\frac{17+\sqrt{209}}{20}
$