9x^2-30x-14=10

Solution for 9x^2-30x-14=10 equation:

9x^2-30x-14=10

We move all terms to the left:

9x^2-30x-14-(10)=0

We add all the numbers together, and all the variables

9x^2-30x-24=0

a = 9; b = -30; c = -24;
Δ = b2-4ac
Δ = -302-4·9·(-24)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-42}{2*9}=\frac{-12}{18}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+42}{2*9}=\frac{72}{18}
=4
$