(14x+58)(10x+50)=180

Solution for (14x+58)(10x+50)=180 equation:

(14x+58)(10x+50)=180

We move all terms to the left:

(14x+58)(10x+50)-(180)=0

We multiply parentheses ..

(+140x^2+700x+580x+2900)-180=0

We get rid of parentheses

140x^2+700x+580x+2900-180=0

We add all the numbers together, and all the variables

140x^2+1280x+2720=0

a = 140; b = 1280; c = +2720;
Δ = b2-4ac
Δ = 12802-4·140·2720
Δ = 115200
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:

$\sqrt{\Delta}=\sqrt{115200}=\sqrt{57600*2}=\sqrt{57600}*\sqrt{2}=240\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1280)-240\sqrt{2}}{2*140}=\frac{-1280-240\sqrt{2}}{280}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1280)+240\sqrt{2}}{2*140}=\frac{-1280+240\sqrt{2}}{280}
$