7x^2+18x=193

Solution for 7x^2+18x=193 equation:

7x^2+18x=193

We move all terms to the left:

7x^2+18x-(193)=0

a = 7; b = 18; c = -193;
Δ = b2-4ac
Δ = 182-4·7·(-193)
Δ = 5728
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:

$\sqrt{\Delta}=\sqrt{5728}=\sqrt{16*358}=\sqrt{16}*\sqrt{358}=4\sqrt{358}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{358}}{2*7}=\frac{-18-4\sqrt{358}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{358}}{2*7}=\frac{-18+4\sqrt{358}}{14}
$