10y^2-15y-54=0*

Solution for 10y^2-15y-54=0* equation:

10y^2-15y-54=0*

We move all terms to the left:

10y^2-15y-54-(0*)=0

We add all the numbers together, and all the variables

10y^2-15y-54-0=0

We add all the numbers together, and all the variables

10y^2-15y-54=0

a = 10; b = -15; c = -54;
Δ = b2-4ac
Δ = -152-4·10·(-54)
Δ = 2385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2385}=\sqrt{9*265}=\sqrt{9}*\sqrt{265}=3\sqrt{265}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{265}}{2*10}=\frac{15-3\sqrt{265}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{265}}{2*10}=\frac{15+3\sqrt{265}}{20}
$