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4x^2=46x+140
We move all terms to the left:
4x^2-(46x+140)=0
We get rid of parentheses
4x^2-46x-140=0
a = 4; b = -46; c = -140;
Δ = b2-4ac
Δ = -462-4·4·(-140)
Δ = 4356
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{4356}=66$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-66}{2*4}=\frac{-20}{8} =-2+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+66}{2*4}=\frac{112}{8} =14 $
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