6x^2=-10x+84

Solution for 6x^2=-10x+84 equation:

6x^2=-10x+84

We move all terms to the left:

6x^2-(-10x+84)=0

We get rid of parentheses

6x^2+10x-84=0

a = 6; b = 10; c = -84;
Δ = b2-4ac
Δ = 102-4·6·(-84)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-46}{2*6}=\frac{-56}{12}
=-4+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+46}{2*6}=\frac{36}{12}
=3
$