2x^2-30=-6x+4

Solution for 2x^2-30=-6x+4 equation:

2x^2-30=-6x+4

We move all terms to the left:

2x^2-30-(-6x+4)=0

We get rid of parentheses

2x^2+6x-4-30=0

We add all the numbers together, and all the variables

2x^2+6x-34=0

a = 2; b = 6; c = -34;
Δ = b2-4ac
Δ = 62-4·2·(-34)
Δ = 308
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{77}}{2*2}=\frac{-6-2\sqrt{77}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{77}}{2*2}=\frac{-6+2\sqrt{77}}{4}
$