5*x*x+3x+8=23

Solution for 5*x*x+3x+8=23 equation:

5x*x+3x+8=23

We move all terms to the left:

5x*x+3x+8-(23)=0

We add all the numbers together, and all the variables

3x+5x*x-15=0

Wy multiply elements

5x^2+3x-15=0

a = 5; b = 3; c = -15;
Δ = b2-4ac
Δ = 32-4·5·(-15)
Δ = 309
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{-(3)-\sqrt{309}}{2*5}=\frac{-3-\sqrt{309}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{309}}{2*5}=\frac{-3+\sqrt{309}}{10}
$