8x2=30+45x

Solution for 8x2=30+45x equation:

8x^2=30+45x

We move all terms to the left:

8x^2-(30+45x)=0

We add all the numbers together, and all the variables

8x^2-(45x+30)=0

We get rid of parentheses

8x^2-45x-30=0

a = 8; b = -45; c = -30;
Δ = b2-4ac
Δ = -452-4·8·(-30)
Δ = 2985
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2985}}{2*8}=\frac{45-\sqrt{2985}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2985}}{2*8}=\frac{45+\sqrt{2985}}{16}
$