18x^2=10x+43

Solution for 18x^2=10x+43 equation:

18x^2=10x+43

We move all terms to the left:

18x^2-(10x+43)=0

We get rid of parentheses

18x^2-10x-43=0

a = 18; b = -10; c = -43;
Δ = b2-4ac
Δ = -102-4·18·(-43)
Δ = 3196
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:

$\sqrt{\Delta}=\sqrt{3196}=\sqrt{4*799}=\sqrt{4}*\sqrt{799}=2\sqrt{799}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{799}}{2*18}=\frac{10-2\sqrt{799}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{799}}{2*18}=\frac{10+2\sqrt{799}}{36}
$