(X-4)(x-10)=35

Solution for (X-4)(x-10)=35 equation:

(X-4)(X-10)=35

We move all terms to the left:

(X-4)(X-10)-(35)=0

We multiply parentheses ..

(+X^2-10X-4X+40)-35=0

We get rid of parentheses

X^2-10X-4X+40-35=0

We add all the numbers together, and all the variables

X^2-14X+5=0

a = 1; b = -14; c = +5;
Δ = b2-4ac
Δ = -142-4·1·5
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{11}}{2*1}=\frac{14-4\sqrt{11}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{11}}{2*1}=\frac{14+4\sqrt{11}}{2}
$