3x2+5x=8

Solution for 3x2+5x=8 equation:

3x^2+5x=8

We move all terms to the left:

3x^2+5x-(8)=0

a = 3; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·3·(-8)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*3}=\frac{-16}{6}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*3}=\frac{6}{6}
=1
$