3x(x-5)=-8

Solution for 3x(x-5)=-8 equation:

3x(x-5)=-8

We move all terms to the left:

3x(x-5)-(-8)=0

We add all the numbers together, and all the variables

3x(x-5)+8=0

We multiply parentheses

3x^2-15x+8=0

a = 3; b = -15; c = +8;
Δ = b2-4ac
Δ = -152-4·3·8
Δ = 129
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{-(-15)-\sqrt{129}}{2*3}=\frac{15-\sqrt{129}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{129}}{2*3}=\frac{15+\sqrt{129}}{6}
$