6x2-49=-7x

Solution for 6x2-49=-7x equation:

6x^2-49=-7x

We move all terms to the left:

6x^2-49-(-7x)=0

We get rid of parentheses

6x^2+7x-49=0

a = 6; b = 7; c = -49;
Δ = b2-4ac
Δ = 72-4·6·(-49)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-35}{2*6}=\frac{-42}{12}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+35}{2*6}=\frac{28}{12}
=2+1/3
$