(4x-10)(2x-7)=75

Solution for (4x-10)(2x-7)=75 equation:

(4x-10)(2x-7)=75

We move all terms to the left:

(4x-10)(2x-7)-(75)=0

We multiply parentheses ..

(+8x^2-28x-20x+70)-75=0

We get rid of parentheses

8x^2-28x-20x+70-75=0

We add all the numbers together, and all the variables

8x^2-48x-5=0

a = 8; b = -48; c = -5;
Δ = b2-4ac
Δ = -482-4·8·(-5)
Δ = 2464
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:

$\sqrt{\Delta}=\sqrt{2464}=\sqrt{16*154}=\sqrt{16}*\sqrt{154}=4\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{154}}{2*8}=\frac{48-4\sqrt{154}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{154}}{2*8}=\frac{48+4\sqrt{154}}{16}
$