6x^2=74x+240

Solution for 6x^2=74x+240 equation:

6x^2=74x+240

We move all terms to the left:

6x^2-(74x+240)=0

We get rid of parentheses

6x^2-74x-240=0

a = 6; b = -74; c = -240;
Δ = b2-4ac
Δ = -742-4·6·(-240)
Δ = 11236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11236}=106$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-106}{2*6}=\frac{-32}{12}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+106}{2*6}=\frac{180}{12}
=15
$