5x2=8x+21

Solution for 5x2=8x+21 equation:

5x^2=8x+21

We move all terms to the left:

5x^2-(8x+21)=0

We get rid of parentheses

5x^2-8x-21=0

a = 5; b = -8; c = -21;
Δ = b2-4ac
Δ = -82-4·5·(-21)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-22}{2*5}=\frac{-14}{10}
=-1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+22}{2*5}=\frac{30}{10}
=3
$