30x^2-40x+20=5x^+4

Solution for 30x^2-40x+20=5x^+4 equation:

30x^2-40x+20=5x^+4

We move all terms to the left:

30x^2-40x+20-(5x^+4)=0

We get rid of parentheses

30x^2-40x-5x^-4+20=0

We add all the numbers together, and all the variables

30x^2-45x+16=0

a = 30; b = -45; c = +16;
Δ = b2-4ac
Δ = -452-4·30·16
Δ = 105
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{105}}{2*30}=\frac{45-\sqrt{105}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{105}}{2*30}=\frac{45+\sqrt{105}}{60}
$