(9x+13+)(10x+15)=180

Solution for (9x+13+)(10x+15)=180 equation:

(9x+13+)(10x+15)=180

We move all terms to the left:

(9x+13+)(10x+15)-(180)=0

We add all the numbers together, and all the variables

(+9x)(10x+15)-180=0

We multiply parentheses ..

(+90x^2+135x)-180=0

We get rid of parentheses

90x^2+135x-180=0

a = 90; b = 135; c = -180;
Δ = b2-4ac
Δ = 1352-4·90·(-180)
Δ = 83025
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:

$\sqrt{\Delta}=\sqrt{83025}=\sqrt{2025*41}=\sqrt{2025}*\sqrt{41}=45\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-45\sqrt{41}}{2*90}=\frac{-135-45\sqrt{41}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+45\sqrt{41}}{2*90}=\frac{-135+45\sqrt{41}}{180}
$