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(5x-22)(8x+46)=90
We move all terms to the left:
(5x-22)(8x+46)-(90)=0
We multiply parentheses ..
(+40x^2+230x-176x-1012)-90=0
We get rid of parentheses
40x^2+230x-176x-1012-90=0
We add all the numbers together, and all the variables
40x^2+54x-1102=0
a = 40; b = 54; c = -1102;
Δ = b2-4ac
Δ = 542-4·40·(-1102)
Δ = 179236
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{179236}=\sqrt{4*44809}=\sqrt{4}*\sqrt{44809}=2\sqrt{44809}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{44809}}{2*40}=\frac{-54-2\sqrt{44809}}{80} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{44809}}{2*40}=\frac{-54+2\sqrt{44809}}{80} $
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