3(x-7)x=10

Solution for 3(x-7)x=10 equation:

3(x-7)x=10

We move all terms to the left:

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

We multiply parentheses

3x^2-21x-10=0

a = 3; b = -21; c = -10;
Δ = b2-4ac
Δ = -212-4·3·(-10)
Δ = 561
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{-(-21)-\sqrt{561}}{2*3}=\frac{21-\sqrt{561}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{561}}{2*3}=\frac{21+\sqrt{561}}{6}
$