6x^2=-25x+91

Solution for 6x^2=-25x+91 equation:

6x^2=-25x+91

We move all terms to the left:

6x^2-(-25x+91)=0

We get rid of parentheses

6x^2+25x-91=0

a = 6; b = 25; c = -91;
Δ = b2-4ac
Δ = 252-4·6·(-91)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-53}{2*6}=\frac{-78}{12}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+53}{2*6}=\frac{28}{12}
=2+1/3
$