111=(10x+58)(6x+41)

Solution for 111=(10x+58)(6x+41) equation:

111=(10x+58)(6x+41)

We move all terms to the left:

111-((10x+58)(6x+41))=0

We multiply parentheses ..

-((+60x^2+410x+348x+2378))+111=0


We calculate terms in parentheses: -((+60x^2+410x+348x+2378)), so:

(+60x^2+410x+348x+2378)

We get rid of parentheses

60x^2+410x+348x+2378

We add all the numbers together, and all the variables

60x^2+758x+2378

Back to the equation:

-(60x^2+758x+2378)


We get rid of parentheses

-60x^2-758x-2378+111=0

We add all the numbers together, and all the variables

-60x^2-758x-2267=0

a = -60; b = -758; c = -2267;
Δ = b2-4ac
Δ = -7582-4·(-60)·(-2267)
Δ = 30484
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:

$\sqrt{\Delta}=\sqrt{30484}=\sqrt{4*7621}=\sqrt{4}*\sqrt{7621}=2\sqrt{7621}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-758)-2\sqrt{7621}}{2*-60}=\frac{758-2\sqrt{7621}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-758)+2\sqrt{7621}}{2*-60}=\frac{758+2\sqrt{7621}}{-120}
$