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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

5(3x-2)x

We multiply parentheses

15x^2-10x

Back to the equation:

-(15x^2-10x)


We get rid of parentheses

-15x^2+10x+10x+5=0

We add all the numbers together, and all the variables

-15x^2+20x+5=0

a = -15; b = 20; c = +5;
Δ = b2-4ac
Δ = 202-4·(-15)·5
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10\sqrt{7}}{2*-15}=\frac{-20-10\sqrt{7}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10\sqrt{7}}{2*-15}=\frac{-20+10\sqrt{7}}{-30}
$