86x^2+90x=223

Solution for 86x^2+90x=223 equation:

86x^2+90x=223

We move all terms to the left:

86x^2+90x-(223)=0

a = 86; b = 90; c = -223;
Δ = b2-4ac
Δ = 902-4·86·(-223)
Δ = 84812
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:

$\sqrt{\Delta}=\sqrt{84812}=\sqrt{4*21203}=\sqrt{4}*\sqrt{21203}=2\sqrt{21203}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{21203}}{2*86}=\frac{-90-2\sqrt{21203}}{172}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{21203}}{2*86}=\frac{-90+2\sqrt{21203}}{172}
$