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4x^2=92-7x
We move all terms to the left:
4x^2-(92-7x)=0
We add all the numbers together, and all the variables
4x^2-(-7x+92)=0
We get rid of parentheses
4x^2+7x-92=0
a = 4; b = 7; c = -92;
Δ = b2-4ac
Δ = 72-4·4·(-92)
Δ = 1521
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{1521}=39$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-39}{2*4}=\frac{-46}{8} =-5+3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+39}{2*4}=\frac{32}{8} =4 $
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