3x^2+22x=35

Solution for 3x^2+22x=35 equation:

3x^2+22x=35

We move all terms to the left:

3x^2+22x-(35)=0

a = 3; b = 22; c = -35;
Δ = b2-4ac
Δ = 222-4·3·(-35)
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{226}}{2*3}=\frac{-22-2\sqrt{226}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{226}}{2*3}=\frac{-22+2\sqrt{226}}{6}
$