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2X(2X-10)+X=90
We move all terms to the left:
2X(2X-10)+X-(90)=0
We add all the numbers together, and all the variables
X+2X(2X-10)-90=0
We multiply parentheses
4X^2+X-20X-90=0
We add all the numbers together, and all the variables
4X^2-19X-90=0
a = 4; b = -19; c = -90;
Δ = b2-4ac
Δ = -192-4·4·(-90)
Δ = 1801
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{-(-19)-\sqrt{1801}}{2*4}=\frac{19-\sqrt{1801}}{8} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{1801}}{2*4}=\frac{19+\sqrt{1801}}{8} $
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