5x2-43x+4=-20

Solution for 5x2-43x+4=-20 equation:

5x^2-43x+4=-20

We move all terms to the left:

5x^2-43x+4-(-20)=0

We add all the numbers together, and all the variables

5x^2-43x+24=0

a = 5; b = -43; c = +24;
Δ = b2-4ac
Δ = -432-4·5·24
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-37}{2*5}=\frac{6}{10}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+37}{2*5}=\frac{80}{10}
=8
$