10x(8x-3)=21

Solution for 10x(8x-3)=21 equation:

10x(8x-3)=21

We move all terms to the left:

10x(8x-3)-(21)=0

We multiply parentheses

80x^2-30x-21=0

a = 80; b = -30; c = -21;
Δ = b2-4ac
Δ = -302-4·80·(-21)
Δ = 7620
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:

$\sqrt{\Delta}=\sqrt{7620}=\sqrt{4*1905}=\sqrt{4}*\sqrt{1905}=2\sqrt{1905}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{1905}}{2*80}=\frac{30-2\sqrt{1905}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{1905}}{2*80}=\frac{30+2\sqrt{1905}}{160}
$