(2x+3)(x+5)=10

Solution for (2x+3)(x+5)=10 equation:

(2x+3)(x+5)=10

We move all terms to the left:

(2x+3)(x+5)-(10)=0

We multiply parentheses ..

(+2x^2+10x+3x+15)-10=0

We get rid of parentheses

2x^2+10x+3x+15-10=0

We add all the numbers together, and all the variables

2x^2+13x+5=0

a = 2; b = 13; c = +5;
Δ = b2-4ac
Δ = 132-4·2·5
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{129}}{2*2}=\frac{-13-\sqrt{129}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{129}}{2*2}=\frac{-13+\sqrt{129}}{4}
$