5x(3+7x)=2

Solution for 5x(3+7x)=2 equation:

5x(3+7x)=2

We move all terms to the left:

5x(3+7x)-(2)=0

We add all the numbers together, and all the variables

5x(7x+3)-2=0

We multiply parentheses

35x^2+15x-2=0

a = 35; b = 15; c = -2;
Δ = b2-4ac
Δ = 152-4·35·(-2)
Δ = 505
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{505}}{2*35}=\frac{-15-\sqrt{505}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{505}}{2*35}=\frac{-15+\sqrt{505}}{70}
$