7x(x-21)=10

Solution for 7x(x-21)=10 equation:

7x(x-21)=10

We move all terms to the left:

7x(x-21)-(10)=0

We multiply parentheses

7x^2-147x-10=0

a = 7; b = -147; c = -10;
Δ = b2-4ac
Δ = -1472-4·7·(-10)
Δ = 21889
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{-(-147)-\sqrt{21889}}{2*7}=\frac{147-\sqrt{21889}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-147)+\sqrt{21889}}{2*7}=\frac{147+\sqrt{21889}}{14}
$