(2x-3)(5x-7)=4x(3x+1)

Solution for (2x-3)(5x-7)=4x(3x+1) equation:

(2x-3)(5x-7)=4x(3x+1)

We move all terms to the left:

(2x-3)(5x-7)-(4x(3x+1))=0

We multiply parentheses ..

(+10x^2-14x-15x+21)-(4x(3x+1))=0


We calculate terms in parentheses: -(4x(3x+1)), so:

4x(3x+1)

We multiply parentheses

12x^2+4x

Back to the equation:

-(12x^2+4x)


We get rid of parentheses

10x^2-12x^2-14x-15x-4x+21=0

We add all the numbers together, and all the variables

-2x^2-33x+21=0

a = -2; b = -33; c = +21;
Δ = b2-4ac
Δ = -332-4·(-2)·21
Δ = 1257
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{-(-33)-\sqrt{1257}}{2*-2}=\frac{33-\sqrt{1257}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1257}}{2*-2}=\frac{33+\sqrt{1257}}{-4}
$