5x^2+3x+2=142

Solution for 5x^2+3x+2=142 equation:

5x^2+3x+2=142

We move all terms to the left:

5x^2+3x+2-(142)=0

We add all the numbers together, and all the variables

5x^2+3x-140=0

a = 5; b = 3; c = -140;
Δ = b2-4ac
Δ = 32-4·5·(-140)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-53}{2*5}=\frac{-56}{10}
=-5+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+53}{2*5}=\frac{50}{10}
=5
$