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(10x+2)(9x+18)=180
We move all terms to the left:
(10x+2)(9x+18)-(180)=0
We multiply parentheses ..
(+90x^2+180x+18x+36)-180=0
We get rid of parentheses
90x^2+180x+18x+36-180=0
We add all the numbers together, and all the variables
90x^2+198x-144=0
a = 90; b = 198; c = -144;
Δ = b2-4ac
Δ = 1982-4·90·(-144)
Δ = 91044
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{91044}=\sqrt{324*281}=\sqrt{324}*\sqrt{281}=18\sqrt{281}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(198)-18\sqrt{281}}{2*90}=\frac{-198-18\sqrt{281}}{180} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(198)+18\sqrt{281}}{2*90}=\frac{-198+18\sqrt{281}}{180} $
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