5x(2)+2(x-3)=42

Solution for 5x(2)+2(x-3)=42 equation:

5x(2)+2(x-3)=42

We move all terms to the left:

5x(2)+2(x-3)-(42)=0

We add all the numbers together, and all the variables

5x^2+2(x-3)-42=0

We multiply parentheses

5x^2+2x-6-42=0

We add all the numbers together, and all the variables

5x^2+2x-48=0

a = 5; b = 2; c = -48;
Δ = b2-4ac
Δ = 22-4·5·(-48)
Δ = 964
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:

$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{241}}{2*5}=\frac{-2-2\sqrt{241}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{241}}{2*5}=\frac{-2+2\sqrt{241}}{10}
$