6.9x^2+21x=15

Solution for 6.9x^2+21x=15 equation:

6.9x^2+21x=15

We move all terms to the left:

6.9x^2+21x-(15)=0

a = 6.9; b = 21; c = -15;
Δ = b2-4ac
Δ = 212-4·6.9·(-15)
Δ = 855
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:

$\sqrt{\Delta}=\sqrt{855}=\sqrt{9*95}=\sqrt{9}*\sqrt{95}=3\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{95}}{2*6.9}=\frac{-21-3\sqrt{95}}{13.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{95}}{2*6.9}=\frac{-21+3\sqrt{95}}{13.8}
$