(-5+28x)(8x+5)=180

Solution for (-5+28x)(8x+5)=180 equation:

(-5+28x)(8x+5)=180

We move all terms to the left:

(-5+28x)(8x+5)-(180)=0

We add all the numbers together, and all the variables

(28x-5)(8x+5)-180=0

We multiply parentheses ..

(+224x^2+140x-40x-25)-180=0

We get rid of parentheses

224x^2+140x-40x-25-180=0

We add all the numbers together, and all the variables

224x^2+100x-205=0

a = 224; b = 100; c = -205;
Δ = b2-4ac
Δ = 1002-4·224·(-205)
Δ = 193680
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:

$\sqrt{\Delta}=\sqrt{193680}=\sqrt{144*1345}=\sqrt{144}*\sqrt{1345}=12\sqrt{1345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-12\sqrt{1345}}{2*224}=\frac{-100-12\sqrt{1345}}{448}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+12\sqrt{1345}}{2*224}=\frac{-100+12\sqrt{1345}}{448}
$