(X-5)(2x-7)=4

Solution for (X-5)(2x-7)=4 equation:

(X-5)(2X-7)=4

We move all terms to the left:

(X-5)(2X-7)-(4)=0

We multiply parentheses ..

(+2X^2-7X-10X+35)-4=0

We get rid of parentheses

2X^2-7X-10X+35-4=0

We add all the numbers together, and all the variables

2X^2-17X+31=0

a = 2; b = -17; c = +31;
Δ = b2-4ac
Δ = -172-4·2·31
Δ = 41
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{-(-17)-\sqrt{41}}{2*2}=\frac{17-\sqrt{41}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{41}}{2*2}=\frac{17+\sqrt{41}}{4}
$