x2+12x-11=7x-8

Solution for x2+12x-11=7x-8 equation:

x2+12x-11=7x-8

We move all terms to the left:

x2+12x-11-(7x-8)=0

We add all the numbers together, and all the variables

x^2+12x-(7x-8)-11=0

We get rid of parentheses

x^2+12x-7x+8-11=0

We add all the numbers together, and all the variables

x^2+5x-3=0

a = 1; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·1·(-3)
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{37}}{2*1}=\frac{-5-\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*1}=\frac{-5+\sqrt{37}}{2}
$