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(9x-22)(5x-7)=180
We move all terms to the left:
(9x-22)(5x-7)-(180)=0
We multiply parentheses ..
(+45x^2-63x-110x+154)-180=0
We get rid of parentheses
45x^2-63x-110x+154-180=0
We add all the numbers together, and all the variables
45x^2-173x-26=0
a = 45; b = -173; c = -26;
Δ = b2-4ac
Δ = -1732-4·45·(-26)
Δ = 34609
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-173)-\sqrt{34609}}{2*45}=\frac{173-\sqrt{34609}}{90} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-173)+\sqrt{34609}}{2*45}=\frac{173+\sqrt{34609}}{90} $
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