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(4x-22)(7x+4)=180
We move all terms to the left:
(4x-22)(7x+4)-(180)=0
We multiply parentheses ..
(+28x^2+16x-154x-88)-180=0
We get rid of parentheses
28x^2+16x-154x-88-180=0
We add all the numbers together, and all the variables
28x^2-138x-268=0
a = 28; b = -138; c = -268;
Δ = b2-4ac
Δ = -1382-4·28·(-268)
Δ = 49060
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{49060}=\sqrt{4*12265}=\sqrt{4}*\sqrt{12265}=2\sqrt{12265}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-2\sqrt{12265}}{2*28}=\frac{138-2\sqrt{12265}}{56} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+2\sqrt{12265}}{2*28}=\frac{138+2\sqrt{12265}}{56} $
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