(-10x+58)(6x+42)=111

Solution for (-10x+58)(6x+42)=111 equation:

(-10x+58)(6x+42)=111

We move all terms to the left:

(-10x+58)(6x+42)-(111)=0

We multiply parentheses ..

(-60x^2-420x+348x+2436)-111=0

We get rid of parentheses

-60x^2-420x+348x+2436-111=0

We add all the numbers together, and all the variables

-60x^2-72x+2325=0

a = -60; b = -72; c = +2325;
Δ = b2-4ac
Δ = -722-4·(-60)·2325
Δ = 563184
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:

$\sqrt{\Delta}=\sqrt{563184}=\sqrt{144*3911}=\sqrt{144}*\sqrt{3911}=12\sqrt{3911}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{3911}}{2*-60}=\frac{72-12\sqrt{3911}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{3911}}{2*-60}=\frac{72+12\sqrt{3911}}{-120}
$