-5x^2+30x+8=34

Solution for -5x^2+30x+8=34 equation:

-5x^2+30x+8=34

We move all terms to the left:

-5x^2+30x+8-(34)=0

We add all the numbers together, and all the variables

-5x^2+30x-26=0

a = -5; b = 30; c = -26;
Δ = b2-4ac
Δ = 302-4·(-5)·(-26)
Δ = 380
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:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{95}}{2*-5}=\frac{-30-2\sqrt{95}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{95}}{2*-5}=\frac{-30+2\sqrt{95}}{-10}
$