x+3x(10+2x)=142

Solution for x+3x(10+2x)=142 equation:

x+3x(10+2x)=142

We move all terms to the left:

x+3x(10+2x)-(142)=0

We add all the numbers together, and all the variables

x+3x(2x+10)-142=0

We multiply parentheses

6x^2+x+30x-142=0

We add all the numbers together, and all the variables

6x^2+31x-142=0

a = 6; b = 31; c = -142;
Δ = b2-4ac
Δ = 312-4·6·(-142)
Δ = 4369
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{-(31)-\sqrt{4369}}{2*6}=\frac{-31-\sqrt{4369}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{4369}}{2*6}=\frac{-31+\sqrt{4369}}{12}
$