(15x+7)+(13x-28)(10x-37)=180

Solution for (15x+7)+(13x-28)(10x-37)=180 equation:

(15x+7)+(13x-28)(10x-37)=180

We move all terms to the left:

(15x+7)+(13x-28)(10x-37)-(180)=0

We get rid of parentheses

15x+(13x-28)(10x-37)+7-180=0

We multiply parentheses ..

(+130x^2-481x-280x+1036)+15x+7-180=0

We add all the numbers together, and all the variables

(+130x^2-481x-280x+1036)+15x-173=0

We get rid of parentheses

130x^2-481x-280x+15x+1036-173=0

We add all the numbers together, and all the variables

130x^2-746x+863=0

a = 130; b = -746; c = +863;
Δ = b2-4ac
Δ = -7462-4·130·863
Δ = 107756
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:

$\sqrt{\Delta}=\sqrt{107756}=\sqrt{4*26939}=\sqrt{4}*\sqrt{26939}=2\sqrt{26939}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-746)-2\sqrt{26939}}{2*130}=\frac{746-2\sqrt{26939}}{260}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-746)+2\sqrt{26939}}{2*130}=\frac{746+2\sqrt{26939}}{260}
$