-19=6(x-5)5x

Solution for -19=6(x-5)5x equation:

-19=6(x-5)5x

We move all terms to the left:

-19-(6(x-5)5x)=0


We calculate terms in parentheses: -(6(x-5)5x), so:

6(x-5)5x

We multiply parentheses

30x^2-150x

Back to the equation:

-(30x^2-150x)


We get rid of parentheses

-30x^2+150x-19=0

a = -30; b = 150; c = -19;
Δ = b2-4ac
Δ = 1502-4·(-30)·(-19)
Δ = 20220
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:

$\sqrt{\Delta}=\sqrt{20220}=\sqrt{4*5055}=\sqrt{4}*\sqrt{5055}=2\sqrt{5055}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-2\sqrt{5055}}{2*-30}=\frac{-150-2\sqrt{5055}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+2\sqrt{5055}}{2*-30}=\frac{-150+2\sqrt{5055}}{-60}
$