7x(2x+3)=2

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

7x(2x+3)=2

We move all terms to the left:

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

We multiply parentheses

14x^2+21x-2=0

a = 14; b = 21; c = -2;
Δ = b2-4ac
Δ = 212-4·14·(-2)
Δ = 553
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{-(21)-\sqrt{553}}{2*14}=\frac{-21-\sqrt{553}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{553}}{2*14}=\frac{-21+\sqrt{553}}{28}
$