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4x*5x+2=112
We move all terms to the left:
4x*5x+2-(112)=0
We add all the numbers together, and all the variables
4x*5x-110=0
Wy multiply elements
20x^2-110=0
a = 20; b = 0; c = -110;
Δ = b2-4ac
Δ = 02-4·20·(-110)
Δ = 8800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8800}=\sqrt{400*22}=\sqrt{400}*\sqrt{22}=20\sqrt{22}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{22}}{2*20}=\frac{0-20\sqrt{22}}{40} =-\frac{20\sqrt{22}}{40} =-\frac{\sqrt{22}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{22}}{2*20}=\frac{0+20\sqrt{22}}{40} =\frac{20\sqrt{22}}{40} =\frac{\sqrt{22}}{2} $
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