6x^2=-5x+144

Solution for 6x^2=-5x+144 equation:

6x^2=-5x+144

We move all terms to the left:

6x^2-(-5x+144)=0

We get rid of parentheses

6x^2+5x-144=0

a = 6; b = 5; c = -144;
Δ = b2-4ac
Δ = 52-4·6·(-144)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-59}{2*6}=\frac{-64}{12}
=-5+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+59}{2*6}=\frac{54}{12}
=4+1/2
$