5x^2-45x+40=(3x+1)(x-2)

Solution for 5x^2-45x+40=(3x+1)(x-2) equation:

5x^2-45x+40=(3x+1)(x-2)

We move all terms to the left:

5x^2-45x+40-((3x+1)(x-2))=0

We multiply parentheses ..

5x^2-((+3x^2-6x+x-2))-45x+40=0


We calculate terms in parentheses: -((+3x^2-6x+x-2)), so:

(+3x^2-6x+x-2)

We get rid of parentheses

3x^2-6x+x-2

We add all the numbers together, and all the variables

3x^2-5x-2

Back to the equation:

-(3x^2-5x-2)


We add all the numbers together, and all the variables

5x^2-45x-(3x^2-5x-2)+40=0

We get rid of parentheses

5x^2-3x^2-45x+5x+2+40=0

We add all the numbers together, and all the variables

2x^2-40x+42=0

a = 2; b = -40; c = +42;
Δ = b2-4ac
Δ = -402-4·2·42
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{79}}{2*2}=\frac{40-4\sqrt{79}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{79}}{2*2}=\frac{40+4\sqrt{79}}{4}
$