6a^2-45a-48=0

Solution for 6a^2-45a-48=0 equation:

6a^2-45a-48=0

a = 6; b = -45; c = -48;
Δ = b2-4ac
Δ = -452-4·6·(-48)
Δ = 3177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3177}=\sqrt{9*353}=\sqrt{9}*\sqrt{353}=3\sqrt{353}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{353}}{2*6}=\frac{45-3\sqrt{353}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{353}}{2*6}=\frac{45+3\sqrt{353}}{12}
$