-8x^2=46x-30=0

Solution for -8x^2=46x-30=0 equation:

-8x^2=46x-30=0

We move all terms to the left:

-8x^2-(46x-30)=0

We get rid of parentheses

-8x^2-46x+30=0

a = -8; b = -46; c = +30;
Δ = b2-4ac
Δ = -462-4·(-8)·30
Δ = 3076
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:

$\sqrt{\Delta}=\sqrt{3076}=\sqrt{4*769}=\sqrt{4}*\sqrt{769}=2\sqrt{769}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{769}}{2*-8}=\frac{46-2\sqrt{769}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{769}}{2*-8}=\frac{46+2\sqrt{769}}{-16}
$