(x+10)(9x)=14x-58

Solution for (x+10)(9x)=14x-58 equation:

(x+10)(9x)=14x-58

We move all terms to the left:

(x+10)(9x)-(14x-58)=0

We multiply parentheses

9x^2+90x-(14x-58)=0

We get rid of parentheses

9x^2+90x-14x+58=0

We add all the numbers together, and all the variables

9x^2+76x+58=0

a = 9; b = 76; c = +58;
Δ = b2-4ac
Δ = 762-4·9·58
Δ = 3688
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:

$\sqrt{\Delta}=\sqrt{3688}=\sqrt{4*922}=\sqrt{4}*\sqrt{922}=2\sqrt{922}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-2\sqrt{922}}{2*9}=\frac{-76-2\sqrt{922}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+2\sqrt{922}}{2*9}=\frac{-76+2\sqrt{922}}{18}
$