-78x2=-591x+546

Solution for -78x2=-591x+546 equation:

-78x^2=-591x+546

We move all terms to the left:

-78x^2-(-591x+546)=0

We get rid of parentheses

-78x^2+591x-546=0

a = -78; b = 591; c = -546;
Δ = b2-4ac
Δ = 5912-4·(-78)·(-546)
Δ = 178929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{178929}=423$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(591)-423}{2*-78}=\frac{-1014}{-156}
=6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(591)+423}{2*-78}=\frac{-168}{-156}
=1+1/13
$