6a^2-10=-7a

Solution for 6a^2-10=-7a equation:

6a^2-10=-7a

We move all terms to the left:

6a^2-10-(-7a)=0

We get rid of parentheses

6a^2+7a-10=0

a = 6; b = 7; c = -10;
Δ = b2-4ac
Δ = 72-4·6·(-10)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*6}=\frac{-24}{12}
=-2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*6}=\frac{10}{12}
=5/6
$