(5x-3)(4x-3)=2(4-5x)+10

Solution for (5x-3)(4x-3)=2(4-5x)+10 equation:

(5x-3)(4x-3)=2(4-5x)+10

We move all terms to the left:

(5x-3)(4x-3)-(2(4-5x)+10)=0

We add all the numbers together, and all the variables

(5x-3)(4x-3)-(2(-5x+4)+10)=0

We multiply parentheses ..

(+20x^2-15x-12x+9)-(2(-5x+4)+10)=0


We calculate terms in parentheses: -(2(-5x+4)+10), so:

2(-5x+4)+10

We multiply parentheses

-10x+8+10

We add all the numbers together, and all the variables

-10x+18

Back to the equation:

-(-10x+18)


We get rid of parentheses

20x^2-15x-12x+10x+9-18=0

We add all the numbers together, and all the variables

20x^2-17x-9=0

a = 20; b = -17; c = -9;
Δ = b2-4ac
Δ = -172-4·20·(-9)
Δ = 1009
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{1009}}{2*20}=\frac{17-\sqrt{1009}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{1009}}{2*20}=\frac{17+\sqrt{1009}}{40}
$