(5x-3)(5x-3)=(4x-7)(4x-7)

Solution for (5x-3)(5x-3)=(4x-7)(4x-7) equation:

(5x-3)(5x-3)=(4x-7)(4x-7)

We move all terms to the left:

(5x-3)(5x-3)-((4x-7)(4x-7))=0

We multiply parentheses ..

(+25x^2-15x-15x+9)-((4x-7)(4x-7))=0


We calculate terms in parentheses: -((4x-7)(4x-7)), so:

(4x-7)(4x-7)

We multiply parentheses ..

(+16x^2-28x-28x+49)

We get rid of parentheses

16x^2-28x-28x+49

We add all the numbers together, and all the variables

16x^2-56x+49

Back to the equation:

-(16x^2-56x+49)


We get rid of parentheses

25x^2-16x^2-15x-15x+56x+9-49=0

We add all the numbers together, and all the variables

9x^2+26x-40=0

a = 9; b = 26; c = -40;
Δ = b2-4ac
Δ = 262-4·9·(-40)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-46}{2*9}=\frac{-72}{18}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+46}{2*9}=\frac{20}{18}
=1+1/9
$