3x(2x-1)+21=5x(3x-2)+1

Solution for 3x(2x-1)+21=5x(3x-2)+1 equation:

3x(2x-1)+21=5x(3x-2)+1

We move all terms to the left:

3x(2x-1)+21-(5x(3x-2)+1)=0

We multiply parentheses

6x^2-3x-(5x(3x-2)+1)+21=0


We calculate terms in parentheses: -(5x(3x-2)+1), so:

5x(3x-2)+1

We multiply parentheses

15x^2-10x+1

Back to the equation:

-(15x^2-10x+1)


We get rid of parentheses

6x^2-15x^2-3x+10x-1+21=0

We add all the numbers together, and all the variables

-9x^2+7x+20=0

a = -9; b = 7; c = +20;
Δ = b2-4ac
Δ = 72-4·(-9)·20
Δ = 769
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{-(7)-\sqrt{769}}{2*-9}=\frac{-7-\sqrt{769}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{769}}{2*-9}=\frac{-7+\sqrt{769}}{-18}
$