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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+28x^2-20x-21x+15)-1x=0

We get rid of parentheses

28x^2-20x-21x-1x+15=0

We add all the numbers together, and all the variables

28x^2-42x+15=0

a = 28; b = -42; c = +15;
Δ = b2-4ac
Δ = -422-4·28·15
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{21}}{2*28}=\frac{42-2\sqrt{21}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{21}}{2*28}=\frac{42+2\sqrt{21}}{56}
$