6x^2-15=89x

Solution for 6x^2-15=89x equation:

6x^2-15=89x

We move all terms to the left:

6x^2-15-(89x)=0

a = 6; b = -89; c = -15;
Δ = b2-4ac
Δ = -892-4·6·(-15)
Δ = 8281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8281}=91$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-91}{2*6}=\frac{-2}{12}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+91}{2*6}=\frac{180}{12}
=15
$