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(5x-22)(3x+42)=180
We move all terms to the left:
(5x-22)(3x+42)-(180)=0
We multiply parentheses ..
(+15x^2+210x-66x-924)-180=0
We get rid of parentheses
15x^2+210x-66x-924-180=0
We add all the numbers together, and all the variables
15x^2+144x-1104=0
a = 15; b = 144; c = -1104;
Δ = b2-4ac
Δ = 1442-4·15·(-1104)
Δ = 86976
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{86976}=\sqrt{576*151}=\sqrt{576}*\sqrt{151}=24\sqrt{151}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-24\sqrt{151}}{2*15}=\frac{-144-24\sqrt{151}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+24\sqrt{151}}{2*15}=\frac{-144+24\sqrt{151}}{30} $
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