8x2=30+43x

Solution for 8x2=30+43x equation:

8x^2=30+43x

We move all terms to the left:

8x^2-(30+43x)=0

We add all the numbers together, and all the variables

8x^2-(43x+30)=0

We get rid of parentheses

8x^2-43x-30=0

a = 8; b = -43; c = -30;
Δ = b2-4ac
Δ = -432-4·8·(-30)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-53}{2*8}=\frac{-10}{16}
=-5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+53}{2*8}=\frac{96}{16}
=6
$