7x(X-10)=140

Solution for 7x(X-10)=140 equation:

7x(x-10)=140

We move all terms to the left:

7x(x-10)-(140)=0

We multiply parentheses

7x^2-70x-140=0

a = 7; b = -70; c = -140;
Δ = b2-4ac
Δ = -702-4·7·(-140)
Δ = 8820
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:

$\sqrt{\Delta}=\sqrt{8820}=\sqrt{1764*5}=\sqrt{1764}*\sqrt{5}=42\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-42\sqrt{5}}{2*7}=\frac{70-42\sqrt{5}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+42\sqrt{5}}{2*7}=\frac{70+42\sqrt{5}}{14}
$