4x+3+2x=5x(x-2)

Solution for 4x+3+2x=5x(x-2) equation:

4x+3+2x=5x(x-2)

We move all terms to the left:

4x+3+2x-(5x(x-2))=0

We add all the numbers together, and all the variables

6x-(5x(x-2))+3=0


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

5x(x-2)

We multiply parentheses

5x^2-10x

Back to the equation:

-(5x^2-10x)


We get rid of parentheses

-5x^2+6x+10x+3=0

We add all the numbers together, and all the variables

-5x^2+16x+3=0

a = -5; b = 16; c = +3;
Δ = b2-4ac
Δ = 162-4·(-5)·3
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{79}}{2*-5}=\frac{-16-2\sqrt{79}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{79}}{2*-5}=\frac{-16+2\sqrt{79}}{-10}
$