9X^2+6x=10

Solution for 9X^2+6x=10 equation:

9X^2+6X=10

We move all terms to the left:

9X^2+6X-(10)=0

a = 9; b = 6; c = -10;
Δ = b2-4ac
Δ = 62-4·9·(-10)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{11}}{2*9}=\frac{-6-6\sqrt{11}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{11}}{2*9}=\frac{-6+6\sqrt{11}}{18}
$