10(x^2-3x)=1

Solution for 10(x^2-3x)=1 equation:

10(x^2-3x)=1

We move all terms to the left:

10(x^2-3x)-(1)=0

We multiply parentheses

10x^2-30x-1=0

a = 10; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·10·(-1)
Δ = 940
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:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{235}}{2*10}=\frac{30-2\sqrt{235}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{235}}{2*10}=\frac{30+2\sqrt{235}}{20}
$