85+69(6x+22)(x+37)=360

Solution for 85+69(6x+22)(x+37)=360 equation:

85+69(6x+22)(x+37)=360

We move all terms to the left:

85+69(6x+22)(x+37)-(360)=0

We add all the numbers together, and all the variables

69(6x+22)(x+37)-275=0

We multiply parentheses ..

69(+6x^2+222x+22x+814)-275=0

We multiply parentheses

414x^2+15318x+1518x+56166-275=0

We add all the numbers together, and all the variables

414x^2+16836x+55891=0

a = 414; b = 16836; c = +55891;
Δ = b2-4ac
Δ = 168362-4·414·55891
Δ = 190895400
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:

$\sqrt{\Delta}=\sqrt{190895400}=\sqrt{900*212106}=\sqrt{900}*\sqrt{212106}=30\sqrt{212106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16836)-30\sqrt{212106}}{2*414}=\frac{-16836-30\sqrt{212106}}{828}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16836)+30\sqrt{212106}}{2*414}=\frac{-16836+30\sqrt{212106}}{828}
$