4x-7x(x-7)=10

Solution for 4x-7x(x-7)=10 equation:

4x-7x(x-7)=10

We move all terms to the left:

4x-7x(x-7)-(10)=0

We multiply parentheses

-7x^2+4x+49x-10=0

We add all the numbers together, and all the variables

-7x^2+53x-10=0

a = -7; b = 53; c = -10;
Δ = b2-4ac
Δ = 532-4·(-7)·(-10)
Δ = 2529
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:

$\sqrt{\Delta}=\sqrt{2529}=\sqrt{9*281}=\sqrt{9}*\sqrt{281}=3\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-3\sqrt{281}}{2*-7}=\frac{-53-3\sqrt{281}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+3\sqrt{281}}{2*-7}=\frac{-53+3\sqrt{281}}{-14}
$