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4x^2=86+7x
We move all terms to the left:
4x^2-(86+7x)=0
We add all the numbers together, and all the variables
4x^2-(7x+86)=0
We get rid of parentheses
4x^2-7x-86=0
a = 4; b = -7; c = -86;
Δ = b2-4ac
Δ = -72-4·4·(-86)
Δ = 1425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1425}=\sqrt{25*57}=\sqrt{25}*\sqrt{57}=5\sqrt{57}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5\sqrt{57}}{2*4}=\frac{7-5\sqrt{57}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5\sqrt{57}}{2*4}=\frac{7+5\sqrt{57}}{8} $
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