5x(x-3)+2=92

Solution for 5x(x-3)+2=92 equation:

5x(x-3)+2=92

We move all terms to the left:

5x(x-3)+2-(92)=0

We add all the numbers together, and all the variables

5x(x-3)-90=0

We multiply parentheses

5x^2-15x-90=0

a = 5; b = -15; c = -90;
Δ = b2-4ac
Δ = -152-4·5·(-90)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-45}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+45}{2*5}=\frac{60}{10}
=6
$