(3x+5)(x+6)=10

Solution for (3x+5)(x+6)=10 equation:

(3x+5)(x+6)=10

We move all terms to the left:

(3x+5)(x+6)-(10)=0

We multiply parentheses ..

(+3x^2+18x+5x+30)-10=0

We get rid of parentheses

3x^2+18x+5x+30-10=0

We add all the numbers together, and all the variables

3x^2+23x+20=0

a = 3; b = 23; c = +20;
Δ = b2-4ac
Δ = 232-4·3·20
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-17}{2*3}=\frac{-40}{6}
=-6+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+17}{2*3}=\frac{-6}{6}
=-1
$