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4(x^2-112x+292)=0
We multiply parentheses
4x^2-448x+1168=0
a = 4; b = -448; c = +1168;
Δ = b2-4ac
Δ = -4482-4·4·1168
Δ = 182016
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{182016}=\sqrt{2304*79}=\sqrt{2304}*\sqrt{79}=48\sqrt{79}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-448)-48\sqrt{79}}{2*4}=\frac{448-48\sqrt{79}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-448)+48\sqrt{79}}{2*4}=\frac{448+48\sqrt{79}}{8} $
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