25(x-3)-2x(x-4)=5x-4

Solution for 25(x-3)-2x(x-4)=5x-4 equation:

25(x-3)-2x(x-4)=5x-4

We move all terms to the left:

25(x-3)-2x(x-4)-(5x-4)=0

We multiply parentheses

-2x^2+25x+8x-(5x-4)-75=0

We get rid of parentheses

-2x^2+25x+8x-5x+4-75=0

We add all the numbers together, and all the variables

-2x^2+28x-71=0

a = -2; b = 28; c = -71;
Δ = b2-4ac
Δ = 282-4·(-2)·(-71)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-6\sqrt{6}}{2*-2}=\frac{-28-6\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+6\sqrt{6}}{2*-2}=\frac{-28+6\sqrt{6}}{-4}
$