(9x+23)(10x+6)=180

Solution for (9x+23)(10x+6)=180 equation:

(9x+23)(10x+6)=180

We move all terms to the left:

(9x+23)(10x+6)-(180)=0

We multiply parentheses ..

(+90x^2+54x+230x+138)-180=0

We get rid of parentheses

90x^2+54x+230x+138-180=0

We add all the numbers together, and all the variables

90x^2+284x-42=0

a = 90; b = 284; c = -42;
Δ = b2-4ac
Δ = 2842-4·90·(-42)
Δ = 95776
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:

$\sqrt{\Delta}=\sqrt{95776}=\sqrt{16*5986}=\sqrt{16}*\sqrt{5986}=4\sqrt{5986}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(284)-4\sqrt{5986}}{2*90}=\frac{-284-4\sqrt{5986}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(284)+4\sqrt{5986}}{2*90}=\frac{-284+4\sqrt{5986}}{180}
$