6x^2-130=-15x-4

Solution for 6x^2-130=-15x-4 equation:

6x^2-130=-15x-4

We move all terms to the left:

6x^2-130-(-15x-4)=0

We get rid of parentheses

6x^2+15x+4-130=0

We add all the numbers together, and all the variables

6x^2+15x-126=0

a = 6; b = 15; c = -126;
Δ = b2-4ac
Δ = 152-4·6·(-126)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-57}{2*6}=\frac{-72}{12}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+57}{2*6}=\frac{42}{12}
=3+1/2
$