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(9x-8)(5x-10)=180
We move all terms to the left:
(9x-8)(5x-10)-(180)=0
We multiply parentheses ..
(+45x^2-90x-40x+80)-180=0
We get rid of parentheses
45x^2-90x-40x+80-180=0
We add all the numbers together, and all the variables
45x^2-130x-100=0
a = 45; b = -130; c = -100;
Δ = b2-4ac
Δ = -1302-4·45·(-100)
Δ = 34900
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{34900}=\sqrt{100*349}=\sqrt{100}*\sqrt{349}=10\sqrt{349}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-10\sqrt{349}}{2*45}=\frac{130-10\sqrt{349}}{90} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+10\sqrt{349}}{2*45}=\frac{130+10\sqrt{349}}{90} $
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