(5x+12)(10x-37)=9x+1

Solution for (5x+12)(10x-37)=9x+1 equation:

(5x+12)(10x-37)=9x+1

We move all terms to the left:

(5x+12)(10x-37)-(9x+1)=0

We get rid of parentheses

(5x+12)(10x-37)-9x-1=0

We multiply parentheses ..

(+50x^2-185x+120x-444)-9x-1=0

We get rid of parentheses

50x^2-185x+120x-9x-444-1=0

We add all the numbers together, and all the variables

50x^2-74x-445=0

a = 50; b = -74; c = -445;
Δ = b2-4ac
Δ = -742-4·50·(-445)
Δ = 94476
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:

$\sqrt{\Delta}=\sqrt{94476}=\sqrt{4*23619}=\sqrt{4}*\sqrt{23619}=2\sqrt{23619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{23619}}{2*50}=\frac{74-2\sqrt{23619}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{23619}}{2*50}=\frac{74+2\sqrt{23619}}{100}
$