(3x+5)(x)=68

Solution for (3x+5)(x)=68 equation:

(3x+5)(x)=68

We move all terms to the left:

(3x+5)(x)-(68)=0

We multiply parentheses

3x^2+5x-68=0

a = 3; b = 5; c = -68;
Δ = b2-4ac
Δ = 52-4·3·(-68)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*3}=\frac{-34}{6}
=-5+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*3}=\frac{24}{6}
=4
$