(5x+7)(3x+23)=100

Solution for (5x+7)(3x+23)=100 equation:

(5x+7)(3x+23)=100

We move all terms to the left:

(5x+7)(3x+23)-(100)=0

We multiply parentheses ..

(+15x^2+115x+21x+161)-100=0

We get rid of parentheses

15x^2+115x+21x+161-100=0

We add all the numbers together, and all the variables

15x^2+136x+61=0

a = 15; b = 136; c = +61;
Δ = b2-4ac
Δ = 1362-4·15·61
Δ = 14836
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14836}=\sqrt{4*3709}=\sqrt{4}*\sqrt{3709}=2\sqrt{3709}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(136)-2\sqrt{3709}}{2*15}=\frac{-136-2\sqrt{3709}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(136)+2\sqrt{3709}}{2*15}=\frac{-136+2\sqrt{3709}}{30}
$